166 coriiVios. 



of -g-g-g-tli. In accordance with this, the polar radius is 1 0,938 

 toises (69,944 feet), or about 11|- miles, shorter than the equa- 

 torial radius of our terrestrial spheroid. The excess at the 

 equator in consequence of the curvature of the upper surface 

 of the globe amounts, consequently, in the direction of gravi- 

 tation, to somevv^hat more than 4^th times the height of 

 Mont Blanc, or only 21 times the probable height of the 

 summit of the Dhawalagiri, in the Himalaya chain. The 

 lunar inequalities (perturbation in the moon'^s latitude and 

 longitude) give, according to the last investigations of Laplace, 

 almost the same result for the eUipticity as the measurements 

 of degrees, viz., 2-y¥^h. The results yielded by the oscillation 

 of the pendulum give, on the whole, a much greater amount 

 of compression, viz., •gjs'th.* 



2-8403 toises, or 18-16 feet, whence the leugtli ofja geographical mile 

 is 3807-23 toises, or 6086-7 feet. Previous combinations of measure- 

 ments of degrees varied betvi^een gl^d and g^^th; thus Walbeck (Z>e 

 Forma et Magnitudine telluris in demensis arcubus Meridiani definiendis, 

 1819) gives 3 Q^ij^th : Ed. Schmidt {Lekrhichder Maikem. und Phi/s. Geo- 

 graphie, 1829, s. 5) gives -ggl^- 2d, as tlie mean of seven measures. Re- 

 specting the influence of great differences of longitude on the polar 

 compression, see Bibliotheqne Universelle, t. xxxiii., p. 181, and t. xxxv., 

 p. 56 ; likev^^ise Connaissance des Term, 1829, p. 290. From the lunar 

 inequalities alone, Laplace {Expositioyi du Syst. dn Monde, p. 229) found 

 it, by tiie older tables of Biirg, to be «'y^th ; and subsequently, from 

 the hmar observations of Burckhardt and Bouvard, he fixed it at ■, g^.yth 

 (M^canique Cileste, t. v., p. 13 and 43). 



* The oscillations of the pendulum give ^^^^th as the general result 

 of Sabine's great expedition (1822 and 1823, from the equator to 80° 

 north latitude) ; according to Freycinet, g^^^.-^d, exclusive of the experi- 

 ments instituted at the Isle of France, Guam, aiad Mowi (Mawi); ac- 

 cording to Forster, ^^^th ; according to Duperrey, ^^^th ; and ac- 

 cording to Liitke ('Partie Nautique, 1836, p. 232), -o^gth, calculated 

 from eleven stations. On the other hand, Mathieu ( Connaiss. des Temps, 

 1816, p. 330) fixed the amount at ^^_d, from observations made be- 

 tween Formentera and Dunkirk; and Biot, at —yth, from observations 

 between Formentera and the island of Unst. Compare Baily, Report 

 on Pendulum Experiments, in the Memoirs of the Royal Astronomical 

 Society, vol. vii., p. 96; also Borenius, in the Bulletin de V Acad, de St. 

 Pitersbourg, 1843, t. i., p. 2.5. The first proposal to apply the length of 

 the pendulum as a standard of measure, and to establish the third part 

 of the seconds pendulum (then supposed to be every where of equal 

 length) as a pes horarius, or general measure, that might be recovered 

 at any age and by all nations, is to be found in Huygens's Horologium 

 Oscillatorium, 1673, Prop. 2.5. A similar wish was afterward publicly 

 expressed, in 1742, on a monument erected at the equator by Bouguer, 

 La Condamine, and Godin. On the beautiful marble tablet which ex- 

 ists, as yet uninjured, in the old Jesuits' College at Quito, I have myself 

 read the inscription, Penduli simplicis (pquinoctialis unius minuti secundt 



