distance must be small when compared with that of the most remote of the bodies which are visible in the heavens. The fixed stars are undoubtedly luminous like the sun; it is therefore probable that they are not nearer to one another than the sun is to the nearest of them. In the milky way and the other starry nebulæ, some of the stars that seem to us to be close to others, may be far behind them in the boundless depth of space; nay, may be rationally supposed to be situate many thousand times farther off; light would therefore require thousands of years to come to the earth from those myriads of suns, of which our own is but 'the dim and remote companion.' SECTION IX. The masses of such planets as have no satellites are known by comparing the inequalities they produce in the motions of the earth and of each other, determined theoretically, with the same inequalities given by observation, for the disturbing cause must necessarily be proportional to the effect it produces. But as the quantities of matter in any two primary planets are directly as the cubes of the mean distances at which their satellites revolve, and inversely as the squares of their periodic times, the mass of the sun and of any planets which have satellites may be compared with the mass of the earth. In this manner it is computed that the mass of the sun is 354936 times that of the earth; whence the great perturbations of the moon, and the rapid motion of the perigee and nodes of her orbit. Even Jupiter, the largest of the planets, is 1050 times less than the sun; or, as was recently deter mined by the perturbations of Juno, appears the 1053-924th part of the sun. The mass of the moon is determined from several sources,-from her action on the terrestrial equator, which occasions the nutation in the axis of rotation; from her horizontal parallax; from an inequality she produces in the sun's longitude, and from her action on the tides. The three first quantities, computed from theory and compared with their observed values, give her mass respectively equal to the,, and part of that of the earth, which do not differ much from each other. Dr. Brinkley, Bishop of Cloyne, has found it to be from the constant of lunar nutation; but from the moon's action in raising the tides, her mass appears to be about the seventy-fifth part of that of the earth, a value that cannot differ much from the truth. 1 692 1 The apparent diameters of the sun, moon, and planets are determined by measurement; therefore their real diameters may be compared with that of the earth; for the real diameter of a planet is to the real diameter of the earth, or 7912 miles, as the apparent diameter of the planet to the apparent diameter of the earth as seen from the planet, that is, to twice the parallax of the planet. The mean apparent diameter of the sun is 1922" 8, and with the solar parallax 8" 577, it will be found that the diameter of the sun is about 886952 miles; therefore if the centre of the sun were to coincide with the centre of the earth his volume would not only include the orbit of the moon, * Professor Airy has recently determined the most accurate estimation of the value of the mass of Jupiter to be deduced 1 1048 69 from the elongation of the fourth satellite: he has also found that the mass of the whole Jovial system is showing how small a proportion the mass of the satellites bears to that of the planet. 1 but would extend nearly as far again, for the moon's mean distance from the earth is about sixty times the earth's mean radius, or 237360 miles: so that twice the distance of the moon is 474960 miles, which differs but little from the solar radius; his equatorial radius is probably not much less than the major axis of the lunar orbit. The diameter of the moon is only 2160 miles; and Jupiter's diameter of 91509 miles is very much less than that of the sun; the diameter of Pallas does not much exceed 79 miles, so that an inhabitant of that planet, in one of our steam-carriages, might go round his world in a few hours. Before entering on the theory of rotation, it may not be thought foreign to the subject to give some idea of the methods of computing the places of the planets, and of forming astronomical tables. Astronomy is now divided into the three distinct departments of theory, observation, and computation. Since the problem of the three bodies can only be solved by approximation, the analytical astronomer determines the position of a planet in space by a series of corrections. Its place in its circular orbit is first found, then the addition or subtraction of the equation of the centre to or from its mean place gives its position in the ellipse; this again is corrected by the application of the principal periodic inequalities; but as these are determined for some particular position of the three bodies, they require to be corrected to suit other relative positions. This process is continued till the corrections become less than the errors of observation, when it is obviously unnecessary to carry the approximation further. By a similar method, the true latitude and distance of the planet from the sun are obtained. All these quantities are given in terms of the time by general analytical formule; they will consequently give the exact place of the body in the heavens, for any time assumed at pleasure, provided they can be reduced to numbers; but before the calculator begins his task, the observer must furnish the necessary data. These are obviously the forms of the orbits, and their positions with regard to the plane of the ecliptic. It is therefore necessary to determine by observation for each planet, the length of the major axis of its orbit, the eccentricity, the inclination of the orbit to the plane of the ecliptic, the longitudes of its perihelion and ascending node at a given time, the periodic time of the planet, and its longitude at any instant, arbitrarily assumed as an origin from whence all its subsequent and antecedent longitudes are estimated. Each of these quantities is determined from that position of the planet on which it has most influence. For example, the sum of the greatest and least distances of the planet from the sun is equal to the major axis of the orbit, and their difference is equal to the eccentricity; the longitude of the planet, when at its least distance from the sun, is the same with the longitude of the perihelion; the greatest latitude of the planet is equal to the inclination of the orbit; and the longitude of the planet, when in the plane of the ecliptic in passing towards the north, is the longitude of the ascending node. But, notwithstanding the excellence of instruments and the accuracy of modern observers, the unavoidable errors of observation can only be compensated by finding the value of each element from the mean of perhaps a thousand, or even many thousands of observations for as it is probable that the errors are not all in one direction, but that some are in excess and others in defect, they will compensate each other when combined. However, the values of the elements determined separately can only be regarded as approximate, because they are so connected that the estimation of any one independently will induce errors in the others, for the eccentricity depends upon the longitude of the perihelion, the mean motion depends upon the major axis, the longitude of the node upon the inclination of the orbit, and vice versa, consequently the place of a planet computed with the approximate data, will differ from its observed place: then the difficulty is to ascertain what elements are most in fault, since the difference in question is the error of all, but that is obviated by finding the errors of some thousands of observations, and combining them so as to correct the elements simultaneously, and to make the sum of the squares of the errors a minimum with regard to each element. The method of accomplishing this depends upon the Theory of Probabilities, a subject fertile in most important results in the various departments of science and of civil life, and quite indispensable in the determination of astronomical data. A series of observations continued for some years will give approximate values of the secular and periodic inequalities, which must be corrected from time to time till theory and observation agree; and when all these quantities are determined in numbers, the longitude, latitude, and distances of the planet from the sun are computed for stated intervals, and formed into tables, arranged according to the time estimated from a given epoch, so that the place of the body may be determined from them. by inspection alone, at any instant, for perhaps a thousand years before and after that epoch. By this tedious process. tables have been computed for eleven planets, besides the moon and the satellites of Jupiter. Those of the four new |
