DENSITY OF THE EAUTH. 161 



expeditions to the most remote parts of both hemispheres." 

 The compression which may be inferred from lunar inequa- 

 lities, affords an advantage not yielded by individual measure- 

 ments of degrees or experiments with the pendulum, since 

 it gives a mean amount which is referable to the whole 

 planet. The comparison of the Earth's compression with 

 the velocity of rotation shows, further, the increase of density 

 from the strata from the surface towards the centre an increase 

 which a comparison of the ratios of the axes of Jupiter and 

 Saturn with their times of rotation, likewise shows to exist in 

 these two large planets. Thus the knowledge of the external 

 form of planetary bodies leads us to draw conclusions regarding 

 their internal character 



The northern and southern hemispheres appear to present 

 nearly the same curvature under equal degrees of latitude, but, 

 as has already been observed, pendulum experiments and mea- 

 surements of degrees yield such different results for individual 

 portions of the Earth's surface that no regular figure can be 

 given which would reconcile all the results hitherto obtained 

 by this method. The true figure of the Earth is to a regular 

 figure as the uneven surfaces of water in motion are to the 

 even surface of water at rest. 



When the Earth had been measured, it still had to be 

 weighed. The oscillations of the pendulum,* and the plummet 

 have here likewise served to determine the mean density of 

 the Earth ; either in connexion with astronomical and geodetic 

 operations, with the view of finding the deflection of the plum- 

 met from a vertical line in the vicinity of a mountain ; or by a 

 comparison of the length of the pendulum in a plain and on 

 the summit of an elevation ; or, finally, by the employment of 

 a torsion-balance, which may be considered as a horizonally 

 vibrating pendulum, for the measurement of the relative density 



* La Cattle's pendulum measurements at the Cape of Good Hope, 

 which have been calculated with much care by Mathieu, (Delambre, Hist, 

 de TAstron. au ISme Siecle, p. 479,) give a compression of 55 \. ? ; but from 

 several comparisons of observations made in equal latitudes in the two 

 hemispheres, (New Holland and the Malouines (Falkland Islands), com- 

 pared with Barcelona, New York, and Dunkirk,) there is as yet no 

 reason for supposing that the mean compression of the southern hemi- 

 sphere is greater than that of the northern. (Biot, in the Mem. dt 

 lAcad. des Sciences, t. viii. 1829, pp. 39-41.) 



M 



