22 COSMOS, 



In addition to the two secondary methods for the direct 

 measurement of a degree on meridian and parallel arcs, we 

 have still to refer to a purely astronomical determination of 

 the figure of the earth. This is based upon the action which 

 the earth exerts upon the motion of the moon, or, in other 

 words, upon the inequalities in lunar longitudes and latitudes. 

 Laplace, who was the first to discover the cause of these in- 

 equalities, has also taught us their application by ingenious- 

 ly showing how they afford the great advantage which indi- 

 vidual measurements of a degree and pendulum experiments 

 are incapable of yielding, namely, that of showing in one 

 single result the mean figure of the earth.* We would here, 

 again, refer to the happy expression of the discoverer of this 

 method, " that an astronomer, without leaving his observa- 

 tory, may discover the individual form of the earth in which 

 he dwells, from the motion of one of the heavenly bodies." 

 After his last revision of the inequalities in the longitude 

 and latitude of our satellite, and by the aid of several thou- 

 sand observations of Burg, Bouvard, and Burckhardt,f La- 

 place found, by means of his lunar method, a compression 



curate geodetical measurement, which is the more important from its 

 serving as a comparison of the levels of the Mediterranean and At- 

 lantic, has been made on the parallel of the chain of the Pyrenees by 

 Coraboeuf, Delcros, and Peytier. 



* Cosmos, vol. i., p. 168. " It is very remarkable that an astrono- 

 mer, without leaving his observatory, may, merely by comparing his 

 observations with analytical results, not only be enabled to determine 

 with exactness the size and degree of ellipticity of the earth, but also 

 its distance from the sun and moon results that otherwise could only 

 be arrived at by long and arduous expeditions to the most remote parts 

 of both hemispheres. The moon may, therefore, by the observation 

 of its movements, render appreciable to the higher departments of as- 

 tronomy the ellipticity of the earth, as it taught the early astronomers 

 the rotundity of our earth by means of its eclipses." (Laplace, Expos, 

 du Syst. du "Monde, p. 230.) We have already in Cosmos, vol. iv., p. 

 145- L46, made mention of an almost analogous optical method sug- 

 gested by Arago, and based upon the observation that the intensity 

 of the ash-colored light that is to say, the terrestrial light in the moon 

 might afford us some information in reference to the transparency 

 of our entire atmosphere. Compare also Airy, in the Encycl. Metrop., 

 p. 189, 236, on the determination of the earth's ellipticity by means 

 of the motions of the moon, as well as at p. 231-235, on the infer- 

 ences which he draws regarding the figure of the earth from preces- 

 sion and nutation. According to Biot's investigations, the latter de- 

 termination would only give, for the earth's ellipticity, limiting and 

 widely differing values (^1^ and -yfg). Astron. Physique, Seme ed., 

 t. ii., 1844, p. 463. 



t Laplace, Mecanique Celeste, ed. de 1846, t. v., p. 1C. 53. 



