sioned by the eruption of elastic fluids formed in its interior, and that the spots are enormous caverns, like the craters of our vol canoes. Light is more intense in the centre of the sun's disc than at the edges, although, from his spheroidal form, the edges exhibit a greater surface under the same angle than the centre does, and therefore might be expected to be more luminous. The fact may be accounted for, by supposing the existence of a dense atmosphere absorbing the rays which have to penetrate a greater extent of it at the edges than at the centre; and accordingly, it appears by Bouguer's observations on the moon, which has little or no atmosphere, that it is more brilliant at the edges than in the centre. 657. A phenomenon denominated the zodiacal light, from its being seen only in that zone, is somehow connected with the rotation of the sun. It is observed before sunrise and after sunset, and is a luminous appearance, in some degree similar to the milky way, though not so bright, in the form of an inverted cone with the base towards the sun, its axis inclined to the horizon, and only inclined to the plane of the ecliptic at an angle of 7°; so that it is perpendicular to the axis of the sun's rotation. Its length from the sun to its vertex varies from 45° to 120°. It is seen under the most favourable circumstances after sunset in the beginning of March: its apex extends towards Aldebaran, making an angle of 64° with the horizon. The zodiacal light varies in brilliancy in different years. It was discovered by Cassini in 1682, but had probably been seen before that time. It was observed in great splendour at Paris on the 16th of February, 1769. 658. The elliptical motion of the planets is occasioned by the action of the sun; but by the law of reaction, the planets must disturb the sun, for the invariable point to which they gravitate is not the centre of the sun, but the centre of gravity of the system; the quantity of motion in the sun in one direction must therefore be equal to that of all the planets in a contrary direction. The sun thus describes an orbit about the centre of gravity of the system, which is a very complicated curve, because it results from the action of a system of bodies, perpetually changing their relative positions; it is such however as to furnish a centrifugal force with regard to each planet, sufficient to counteract the gravitation towards it. Newton has shown that the diameter of the sun is nearly equal to 0.009 of the radius of the earth's orbit. If all the great planets of the system were in a straight line with the sun, and on the same side of him, the centre of the sun would be nearly the farthest possible from the common centre of gravity of the whole; yet it is found by computation, that the distance is not more than 0.0085 of the radius vector of the earth; so that the centre of the sun is never distant from the centre of gravity of the system by as much as his own dia meter. Influence of the Fixed Stars in disturbing the Solar System. 659. It is impossible to estimate the effects of comets in disturbing the solar system, on account of our ignorance of the elements of their orbits, and even of the existence of such as have a great perihelion distance, which nevertheless may trouble the planetary motions; but there is every reason to believe that their masses are too small to produce a sensible influence; the effect of the fixed stars may, however, be determined. Let m' be the mass of a fixed star, x', y', z', its co-ordinates referred to the centre of gravity of the sun, and r' its distance from that point. Also let x, y, z, be the co-ordinates of a planet m, and r its radius vector; then the disturbing influence of the star is when developed according to the powers of r'. The fixed plane being the orbit of m at the epoch, then x = r cos v, y=r sin v, 2 = rs, let I be the latitude of the fixed star, and u its longitude, then xr.cos l. cos u, y' = r. cos l. sin u, z' = r'. sin l; and if all the powers of r' above the cube be omitted, it will be found that a But But neglecting s, the substitution of this in equation (155) gives .{(1-cos2)e sin(v-w)-cos2l.e.sin(v+w-2u)}. whence = de cos (vw) + edw. sin (v Whence it appears, that the star occasions secular variations in the eccentricity and longitude of the perihelion of m, but these variations are incomparably less than those caused by the planets. For if m be the earth, the distance of the star from the centre of the sun cannot be less than 100,000 times the mean distance of the earth from the sun, because the annual parallax of the nearest fixed star is less than 1"; therefore assuming r' 100,000.a the coefficient m'a3 -nt does not exceed 0".0000000013. m't,t being any number of Julian years. This quantity is incomparably less than the corresponding variation in the eccentricity of the earth's orbit, arising from the action of the planets, which is unless the mass m' of the fixed stars be much greater than what is probable. Whence it may be concluded that the attraction of the fixed stars has no sensible influence on the form of the planetary orbits; and it may be easily proved, that the positions of the orbits are also uninfluenced. Disturbing Effect of the Fixed Stars on the Mean Motions of the Planets. 660. The part of equation (156) that depends on R, when μ-1, is d.dg safndt.dR 2a.ndt.r dR dr s.sin 21. cos (v-u) which is the whole variation in the mean motion of m from the action of the fixed stars. The parts will be examined separately. Let r' and ' be the distance and latitude of the star at the epoch 1750, and let it be assumed, that these quantities diminish annually by a and B, then t being any indefinite time, and I become pl = p''(1 - at), l = l'(1- Bt) We know nothing of the changes in the distance of the fixed stars; but with regard to the earth, they may be assumed to vary 0".324 annually in latitude; a quantity inappreciable from the earliest observations. With regard to the terms in s, dp dt dq t. cos v; dt But with regard to the earth P= 0".076721.t. +0".000021555.t 9= 0.50096.t + 0".0000067474 . ť. If these quantities be substituted, it will be found that the secular inequalities in the mean motion of the earth are quite insensible; the earliest records also prove them to be so. The same results will be obtained for the most distant planets, whence it may be concluded that the fixed stars are too remote to affect the solar system. Construction of Astronomical Tables. 661. The motion of a planet in longitude consists of three parts, of the mean or circular motion; of a correction depending on the eccentricity, which is the equation of the centre; and of the periodic inequalities. In the construction of tables, the mean longitude of the body, and the mean longitude of the aphelion, or perihelion, are determined in degrees, minutes, seconds, and tenths, at the instant assumed as the origin of the tables. These initial values are generally computed for the beginning of each year, and are called the epoch of the tables; from them subsequent values are deduced at convenient intervals, by adding the daily increments. These intervals are longer or shorter according to the motion of the body, or its importance, and the intermediate values are found by simple proportion, or by tables of proportional parts. The mean anomaly is given by the tables, since it is the difference between the mean longitudes of the body and of the aphelion. The tables of the equation of the centre, and of the mean longitude of the aphelion, give these quantities for each degree of mean anomaly. To these are added tables of the periodic inequalities in longitude, and of the secular inequalities in the eccentricity and longitude of the aphelion. From these tables the true longitude of the body may be known at any instant, by applying the corrections to the mean longitude. The radius vector consists of three parts,-of a mean value, which is equal to half the greater axis of the orbit; of the elliptical variations, and of its periodic inequalities. The two latter are given in the tables for every degree of mean anomaly. The latitude is computed in terms of the mean anomaly at stated intervals: besides these, the |
