148 LAPLACE. 



aduiiratiou. The reader will excuse me for citiuff auotber of such ex- 

 amples. 



The earth governs the movements of the moon. The earth is flattened ; 

 ju other words, its figure is spheroidal. A spheroidal body does not at- 

 tract like a sphere. There ought, then, to exist iu the movement, 1 had 

 almost said in the countenance, of the moon a sort of impression of the 

 spheroidal figure of the earth. Such was the idea as it originally oc- 

 curred to Laplace. 



It still remained to ascertain (and here consisted the chief difiQculty) 

 whether the effects attributable to the spheroidal figure of the earth 

 were sufficiently sensible not to be confounded with the errors of obser- 

 vation. It was accordingly necessary to find the general formula of per- 

 turbations of this nature, in order to be able, as in the case of the solar 

 parallax, to eliminate the unknown quantity. 



The ardor of Laplace, combined with his power of analytical research, 

 surmounted all obstacles. By means of an investigation which de- 

 manded the most minute attention^ the great geometer discovered in 

 the theory of the moon's movements two well-defined perturbations de- 

 pending on the spheroidal figure of the earth. The first affected the 

 resolved element of the motion of our satellite, which is chiefly measured 

 with the instrument known in observatories by the name of the transit 

 instrument; the second, which operated iu the direction north and south, 

 could only be effected by observations with a second instrument, termed 

 the mural circle. These two inequalities, of very different magnitudes, 

 connected with the cause which produces them, by analytical combina- 

 tions of totally different kinds, have, however, both conducted to the 

 same value of the ellipticity. It must be borne iu mind, however, that 

 the ellipticity, thus deduced from the movements of the moon, is not 

 the ellipticity corresponding to such or such a country, the ellipticity 

 observed in France, in England, in Italy, in Lapland, in Xorth America, 

 in India, or in the region of the Cape of Good Hope, for the earth's ma- 

 terials having undergone considerable upheavings at different times, 

 and in different places, the primitive regularity of its curvature has been 

 sensibly disturbed by this cause. The moon — and it is this circumstance 

 which renders the result of such inestimable value — ought to assign, 

 and has in reality assigned, the general ellipticity of the earth ; in other 

 words, it has indicated a sort of mean value of the various determina- 

 tions obtahied at enormous expense, and with infinite labor, as the 

 result of long voyages undertaken by astronomers of all the countries 

 of Europe. 



1 shall add a few brief remarks, for which I am mainly indebted to 

 the author of the M6canique Celeste. They seem to be eminently 

 adapted for illustrating the profound, the unexpected, and almost par- 

 adoxical character of the methods which I have just attempted to^ 

 sketch. 



What are the elements which it has been found necessary to confront 



