328 FIGURE OF THE EARTH. 



exactness, or, at least, close approximation of the number j^-^j, is found, more- 

 over, to be confirmed by another class of considerations extraneous, in a certain 

 degree, to geodesy, and very indirectly related to those which served the two 

 celebrated astronomers last mentioned as a basis and guide in their valuable 

 labors of c()ml)ination and analysis. 



It was remarked at the close of the second pai't of the present article that 

 nothing in nature is fortuitous ; and it might well have been added that not only 

 is nothing fortuitous, but there is nothing without a reason for its being as it is, 

 nothing susceptible of being essentially modifi(!d without communicating an 

 impression to oiher organic parts of the complicated mechanism of the universe. 

 The movement by which the moon is carried around the eartli does not dept>nd 

 exclusively on the intervening distance or the respective masses of the two 

 bodies, but on tli(^ distribution of their masses in concentric groups or on the 

 figure of both globes. If the earth were spherical, the movement of its satel- 

 lite would not be that which is always observed; nor if the discrepancy from 

 that simple form had been represented by a fraction differing from g-i^- would 

 this fact have failed to disclose itself in a degree more or less sensible in some 

 of the accidents which characterize the lunar movement : theory, based upon 

 the laws of universal attraction, laws announced by Newton and so sagaciously 

 developed by Laplace, indicated the orbit which the moon was destined to de- 

 scribe on the hypothesis of the polar depression of our globe being less by -^^ 

 than the equatorial radius, and observation promjitly confirmed all the conclu- 

 sions to which the theory had pointed. Few astronomical discoveries reflect 

 more honor on the human intellect than the valuatioti of the earth's ellipticity 

 based upon the principles which have been just cursorily mentioned. 



But it is not necessary to withdraAV our eyes from the globe we inhabit to 

 discover other means, besides those which are strictly geodesical, not only of 

 demonstrating the ellipticity of its form, but of verifying the limits within 

 which the eccentricity of that new figure is comprised. Our readers will doubt- 

 less readily infer that the process alluded to consists in the use of the pendu- 

 lum, whose oscillations are more or less rapid in different parts of the earth, 

 by reason of its form being sensibly and essentially different from the spheri- 

 cal. When Laplace announced the relation existing between the movement of 

 the moon and the oblateness of the earth, Olairault, in a special treatise on the 

 subject, had already stated the law of interdependence by which the continu- 

 ous depression of the globe from the equator to the poles is associated with 

 the variations of gravitation or of the weight of bodies, and consequently with 

 the oscillatory movement of a pendulum on the surface of that globe. By both 

 geometers the task of verifying tlic truth of their theories was bequeathed to 

 after experiment, and in both cases the previsions of mathematical analysis and 

 the results of observations long and carefully repeated have been found to be 

 perfectly accordant. 



In the long period which elapsed from the date when the French academician 

 Richer first noticed the retardation of the pendulum in the equatorial zone, 

 to that when the Spanish admiral, Malespina, undertook his justly celebrated 

 voyage of scientific exploration in 1789, the experiments made with the pendu- 

 lum were numcn-ous and interesting, in so far as they were directed to the 

 demonstration of the ellipticity of the earth and the accidental irregularities 

 which distinguish it; but those undertaken with a view to determine the value 

 of that ellipticity have been neither so many nor were they so early as the 

 former. In 182G Bcssel showed the inaccuracy or want of care in the process 

 till then followed for deducing from the oscillations or length of a compound 

 pendulum, moving in air and at a variable temperature, the corresponding ele- 

 ments of a simjde pendulum, oscillating in a vacuum and in a thennal state of 

 absolute invariability ; and, even much later, Humboldt thought that experi- 

 ments Avith the pendulum, comparable in delicacy and precision with the 



