THE FIGURE OF THE EARTH. 317 
thetic 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.* When in 
attempting the solution of great problems we have re- 
course to such simplifications; when, in order to elude 
difficulties of calculation, we depart so widely from natu- 
ral 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 re- 
semblance between the forms of the superposed and un- 
equally 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 im- 
mediate 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 measure- 
ment. The earth, then, was originally fluid: analysis 
* 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. 
