All this was quite true, but Newton did not succeed in establishing it by a mathematical process.  Now this great man had introduced into philosophy the severe and just rule:  Consider as certain only what has been demonstrated.  The demonstration of the Newtonian conception of the precession of the equinoxes was, then, a great discovery, and it is to D’Alembert that the glory of it is due.[27] The illustrious geometer gave a complete explanation of the general movement, in virtue of which the terrestrial axis returns to the same stars in a period of about 26,000 years.  He also connected with the theory of gravitation the perturbation of precession discovered by Bradley, that remarkable oscillation which the earth’s axis experiences continually during its movement of progression, and the period of which, amounting to about eighteen years, is exactly equal to the time which the intersection of the moon’s orbit with the ecliptic employs in describing the 360 deg. of the entire circumference.

Geometers and astronomers are justly occupied as much with the figure and physical constitution which the earth might have had in remote ages as with its present figure and constitution.

As soon as our countryman Richer discovered that a body, whatever be its nature, weighs less when it is transported nearer the equatorial regions, everybody perceived that the earth, if it was originally fluid, ought to bulge out at the equator.  Huyghens and Newton did more; they calculated the difference between the greatest and least axes, the excess of the equatorial diameter over the line of the poles.[28]

The calculation of Huyghens was founded upon hypothetic properties of the attractive force which were wholly inadmissible; that of Newton upon a theorem which he ought to have demonstrated; the theory of the latter was characterized by a defect of a still more serious nature:  it supposed the density of the earth during the original state of fluidity, to be homogeneous.[29] When in attempting the solution of great problems we have recourse to such simplifications; when, in order to elude difficulties of calculation, we depart so widely from natural and physical conditions, the results relate to an ideal world, they are in reality nothing more than flights of the imagination.

In order to apply mathematical analysis usefully to the determination of the figure of the earth it was necessary to abandon all idea of homogeneity, all constrained resemblance between the forms of the superposed and unequally dense strata; it was necessary also to examine the case of a central solid nucleus.  This generality increased tenfold the difficulties of the problem; neither Clairaut nor D’Alembert was, however, arrested by them.  Thanks to the efforts of these two eminent geometers, thanks to some essential developments due to their immediate successors, and especially to the illustrious Legendre, the theoretical determination of the figure of the earth has attained all desirable perfection.  There now reigns the most satisfactory accordance between the results of calculation and those of direct measurement.  The earth, then, was originally fluid:  analysis has enabled us to ascend to the earliest ages of our planet.[30]