radii, we shall perceive that this curve is not exactly circular, but that it is somewhat elongated in the direction of the straight line which, passing through the centre of the Earth, joins the points of the greatest and least distance of the Sun. The resemblance of this curve to an ellipse, having led to a comparison with it, their identity has been recognised, from whence this conclusion has been established, that the solar orbit is an ellipse, of which the centre of the earth occupies one of the foci. The ellipse is one of those celebrated curves, both in ancient and modern geometry, which being formed by the section of a surface of the cone by a plane, have been called conic sections. It is easy to describe it by fixing the extremities of a thread upon two immovable points, which thread being stretched upon a plane by a point which slides along it, the curve traced by the point in this motion is an ellipse, it is evidently elongated in the direction of which being prolonged on each side till it meets the curve forms the greater axis, whose length is equal to that of the thread. The greater axis divides the ellipse into two equal and similar parts, the lesser axis is the straight line drawn through the centre and prolonged each way till it meets the curve; the distance from the centre to one of the foci, is the excentricity of the ellipse; when the two foci become united in one point the ellipse becomesa circle; by separating them the ellipse gradually lengthens, and when the distance of the foci becomes infinite, the distance of the focus to the nearest summit of the curve remains finite, and the ellipse becomes a parabola. The solar ellipse differs but little from a circle, for its excentricity is evidently the excess of the greatest above the mean distance of the Sun from the Earth; which excess we have seen is equal to one hundred and sixty-eight ten-thousandths of this distance. Observations seem to indicate in this excentricity, a very slow diminution, and scarcely perceptible in a century. To have a just idea of the elliptic motion of the Sun, let us conceive a point mo' ved uniformly in the circumference of a circle, of which the centre is that of the Earth, and whose radius is equal to the distance perigee of the Sun. Suppose, moreover, that this point and the Sun, set off together from the perigee, and that the angular motion of the point is equal to the mean angular motion of the Sun. Whilst the radius vector of the point revolves uniformly round the Earth, the radius vector of the Sun moves in an unequal manner, by forming always with the distance perigee, and the arcs of the ellipse, sectors proportional to the times. At first it will precede the radius vector of the point, and make an angle with it, which after having augmented to a certain limit will diminish and become nothing; when the Sun is at the apogee, then the two radii will coincide with the greater axis. In the second half of the ellipse the radius vector of the point will precede the radius vector of the Sun and form with it angles, which are exactly the same as in the first half, at the same distance from the perigee, where it will again coincide with the radius vector of the Sun and the greater axis of the ellipse. The angle by which the radius vector of the Sun precedes the radius vector of the point is called the equation of the centre; its maximum, or greatest equation of the centre, was in 1750 equal * 2o1409. The angular motion of the point round the earth is concluded from the length of an entire revolution of the Sun in its orbit; by applying to this the equation of the centre, we obtain the angular motion of the Sun. The investigation of this equation is an interesting problem in analysis, which cannot be solved but by approximation; but the small excentricity of the solar orbit, leads to series, which converge rapidly, and are easily reduced to the form of tables. * 1 55′ 36′′ 4. The position of the greater axis of the solar ellipse is not constant. The angular distance of the perigee, to the equinox of spring reckoned in the direction of the Sun's motion was in the beginning of 1750 = *309° 5790, but it has relatively to the fixed stars an annual motion of about 36′′7, in the same direction as that of the Sun. The solar orbit approaches by insensible degrees to the equator; the secular diminution of its obliquity to the plane of this great circle may be estimated at about 154" 3. The elliptic motion of the Sun, will not exactly represent modern observations their extreme precision has discovered small inequalities of which it would have been almost impossible by observation alone tohave developed the laws. The investigation of these inequalities belongs to that branch of astronomy, which re-descends from |