From the lunar theory, the mean distance of the sun from the earth, and thence the whole dimensions of the solar system, are known; for the forces which retain the earth and moon in their orbits are respectively proportional to the radii vectores of the earth and moon, each being divided by the square of its periodic time. And, as the lunar theory gives the ratio of the forces, the ratio of the distances of the sun and moon from the earth is obtained. Hence it appears that the sun’s mean distance from the earth is 399·7 or nearly 400 times greater than that of the moon. The method of finding the absolute distances of the celestial bodies, in miles, is in fact the same with that employed in measuring the distances of terrestrial objects. From the extremities of a known base (N. 116), the angles which the visual rays from the object form with it are measured; their sum subtracted from two right angles gives the angle opposite the base; therefore, by trigonometry, all the angles and sides of the triangle may be computed—consequently the distance of the object is found. The angle under which the base of the triangle is seen from the object is the parallax of that object. It evidently increases and decreases with the distance. Therefore the base must be very great indeed to be visible from the celestial bodies. The globe itself, whose dimensions are obtained by actual admeasurement, furnishes a standard of measures with which we compare the distances, masses, densities, and volumes of the sun and planets. SECTION VI. Form of the Earth and Planets—Figure of a Homogeneous Spheroid in Rotation—Figure of a Spheroid of variable Density—Figure of the Earth, supposing it to be an Ellipsoid of Revolution—Mensuration of a Degree of the Meridian—Compression and Size of the Earth from Degrees of Meridian—Figure of Earth from the Pendulum.