DENSlTi OF THE EARTH. 169 



The compression which may be inferred from lunar inequali- 

 ties affords an advantage not yielded by individual measure- 

 ments of degrees or experiments with the pendulum, since it 

 cives a. mean amount which is referable to the whole planet. 

 The comparison of the Earth's compression with the velocity 

 nf rotation shows, further, the increase of density from the 

 strata from the surface toward the center 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 

 measurements of degrees yield such different results for indi- 

 vidual 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 bo 

 weighed. The oscillations of the pendulum* and the plum- 

 met have here likewise served to determine the mean density 

 of the Earth, either in connection with astronomical and geo- 

 detic operations, with the view of finding the deflection of the 

 plummet 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 horizon- 

 tally vibrating pendulum for the measurement of the relative 

 density of neighboring strata. Of these three methods! the 



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

 which have been calculated with much care by Mathieu (Delambre. 

 Hitt. de FAstron. au ISme Siecle, p. 479), give a compression of ^j.jth ; 

 but, from several comparisons of observations made in equal latitudes 

 u the two hemispheres (New Holland and the Malouines (Falkland 

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

 as yet no reason for supposing that the mean compression of the south* 

 cm hemisphere is greater than that of the northern. (Biot, in the Mm. 

 de VAcad. det Sciences, t. viii., 1829, p. 39-41.) 



t The three methods of observation give the following results: (1.) by 

 the deflection of the plumb-line in the proximity 01 the Shehallien 

 Mountain (Gaelic, Thichallin) in Perthshire, 4'713, as determined by 

 Maskelyne, Hutton, and Play fair (1774-177G and 1810), according to a 

 method that had been proposed by Newton: (2.) by pendulum vibra 

 VOL. I II 



