great depths, through open clefts, and approached near the surface. In the astronomical part of the determination of degrees of latitude, mountain chains, or the denser strata of the Earth, likewise exercise, although in a less degree, an unfavorable influence on the measurement. As the form of the Earth exerts a powerful influence on the motions of other cosmical bodies, and especially on that of its own neighboring satellite, a more perfect knowledge of the motion of the latter will enable us reciprocally to draw an inference regarding the figure of the Earth. Thus, as Laplace ably remarks,* "An astronomer, without leaving his observatory, may, by a comparison of lunar theory with true observations, not only be enabled to determine the form and size of the Earth, but also its distance from the Sun and Moon -- results that otherwise could only be arrived at by long and arduous expeditions to the most remote parts of both hemispheres." [footnote] *Laplace, 'Expos. du Syst. du Monde', p. 231. p 169 The compression which may be inferred from lunar inequalities affords an advantage not yielded by individual measurements 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 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 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 on 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 connection with astronomical and geodetic 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 horizontally vibrating pendulum for the measurement of the relative density of neighbouring strata.