xlvi 



NOTES. 



ou the vibrations of the pendulum were given by Thomas Young, in the Phil. 

 Trans, for 1819, pp. 70 96. But in drawing conclusions from the length 

 of the pendulum relatively to the curvature of the earth, it ought not to be 

 overlooked that the crust of the earth may possibly have been hardened pre- 

 vious to metallic and dense basaltic masses having penetrated from great 

 depths through open channels and clefts, and approached the surface. 



( 134 ) p. 158. Laplace, Expos, du Systeme du Monde, p. 231. 



( 135 ) p. 159. La Caille's pendulum experiments at the Cape of Good Hope, 

 which Mathieu has calculated with great care (Delambre, Hist, de 1'Astr. an 

 18 me siecle, p. 479), give an ellipticity of 5^.7; fr m several comparisons of 

 observations in equal latitudes in the two hemispheres (New Holland and the 

 Falkland Islands compared with Barcelona, New York, and Dunkirk), there is 

 as yet no ground for supposing the mean ellipticity of the southern hemisphere 

 to be greater than that of the northern (Biot, in the Mem. de 1'Acad. des 

 Sciences, T. viii. 1829, pp. 3941). 



( 136 ) p. 159. The three methods of observation give the following results : 

 1st, from the deflection of the plumb-line by the proximity of the Schehallien 

 Mountain (Gaelic, Thichallin), in Perthshire, 4'713, resulting from the expe- 

 riments of Maskelyne, Hutton, and Playfair, 1774 1776 and 1810) according 

 to a method which had been proposed by Newton ; 2d, by pendulum vibra- 

 tions on a mountain, 4'837 (Carlini's observations on Mount Cenis compared 

 with Biot's observations at Bordeaux, Effemer. astr. di Milano, 1824, p. 184) ; 

 3d, by the balance of torsion in Cavendish's experiments with an apparatus 

 originally devised by Mitchell, 5'48 ; or, according to Huttou's revision of 

 the calculation, 5'32, or Eduard Schmidt's revision, 5'52 (Lchrbuch der 

 math. Geographic, Bd. i. S. 487) ; by the balance of torsion in Reich's expe- 

 riments, 5'44. In the calculation of these experiments of Professor Reich, 

 which are a model of exactness, the original mean result (having a probable 

 error of only 0'0233) was 5'43 ; which, being increased by the quantity by 

 which the centrifugal force of the earth diminishes, the force of gravity for 

 the latitude-of Freiberg (50 55') becomes 5'44. The employment of masses 

 of cast iron instead of lead has not shewn any sensible difference, or none which 

 Ls not well within the limits of observation error, disclosing therefore no traces 

 of magnetic influence (Reich, Versuche iiber die mittlere Dichtigkeit der Erde, 

 1838, S. 60, 62, und 66). By the assumption of too small an ellipticity 

 of the earth in the calculations, and by the difficulty of forming a correct 

 estimate of the density of rocks on the surface, the mecn density of the earth, 

 previously deduced from the experiments on or near mountains, appeared^ too 



