FIGURE OF THE EARTH. 157 



in the exactness of instruments (as those employed in the 

 measurements of space) in optical and chronological observa- 

 tions; to greater perfection in the fundamental branches of 

 astronomy and mechanics in respect to lunar motion and to 

 the resistance experienced by the oscillations of the pendu- 

 lum; and to the discovery of new and hitherto untrodden 

 paths of analysis. With the exception of the investigations 

 of the parallax of stars, which led to the discovery of aberra- 

 tion and nutation, the history of science presents no problem 

 in which the object attained the knowledge of the compres- 

 sion and of the irregular form of our planet is so far exceeded 

 in importance by the incidental gain which has accrued, 

 through a long and weary course of investigation, in the 

 general furtherance and improvement of tne mathematical 

 and astronomical sciences. The comparison of eleven mea- 

 surements of degrees, (in which are included three extra-Eu- 

 ropean namely, the old Peruvian, and two East Indian,) 

 gives, according to the most strictly theoretical requirements 

 allowed for by Bessel,* a compression of -^-J-g- . In accordance 

 with this, the polar radius is 10,938 toises (69,944 feet), or 

 about 11-}- miles, shorter than the equatorial radius of our 



* According to Bessel's examination of ten measurements of degrees, 

 in which the error discovered by Puissant in the calculation of the 

 French measurements is taken into consideration, (Schumacher, Astron. 

 Nadir., 1841, Nr. 438, s. 116,) the semi-axis major of the elliptical 

 spheroid of revolution to which the irregular figure of the Earth most 

 closely approximates, is 3,272,077'14 toises, or 20,924,774 feet; the 

 semi-axis minor, 3,261,159'83 toises, or 20,854,821 feet; and the 

 amount of compression or eccentricity, 25 g 1 . T 5 5 ; the length of a mean 

 degree of the meridian, 57,013109 toises, or 364,596 feet, with an error 

 of + 2'8403 toises, or 18'16 feet, whence the length of a geographical 

 mile is 3807'23 toises, or 60867 feet. Previous combinations of measure- 

 ments of degrees varied between g ?, 7 and ^: thus Walbeck (De 

 Forma, et Magnitudine telluris in demensis arcubus Meridiani de^ 

 finiendis, 1819,) gives 3^: Ed. Schmidt, (Lehrbuch der mathem. und 

 phys. Geographic, 1829, s. 5,) gives ^^, as the mean of seven mea- 

 sures. Respecting the influence of great differences of longitude on the 

 polar compression, see BiUiotlieque Universelle, t. xxxiii. p. 181, and 

 t. xxxv. p. 56; likewise Connaissance des Terns, 1829, p. 290. From 

 the lunar inequalities alone, Laplace (Exposition dy, Syst. du Monde, p. 

 229) found it, by the older tables of Burg, to be 3^3; and subsequently 

 from the lunar observations of Burckhardt and Bouyard, he fixed it 

 at m-i> (Mecaniyuz celeste, t. v. pp. 13 and 43.) 



