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, 



