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been the case, without any great change in the form of the terrestrial spheroid. The variation in the length of the pendulum was first remarked by Richter in 1672, while observing transits of the fixed stars across the meridian at Cayenne, about five degrees north of the equator. He found that his clock lost at the rate of 2m 28 daily, which induced him to determine the length of a pendulum beating seconds in that latitude; and repeating the experiments on his return to Europe, he found the seconds' pendulum at Paris to be more than the twelfth of an inch longer than that at Cayenne. The form and size of the earth being determined, a standard of measure is furnished with which the dimensions of the solar system may be compared.

SECTION VII.

Parallax-Lunar Parallax found from direct Observation-Solar Parallax deduced from the Transit of Venus-Distance of the Sun from the Earth-Annual Parallax-Distance of the Fixed Stars.

THE parallax of a celestial body is the angle under which the radius of the earth would be seen, if viewed from the center of that body; it affords the means of ascertaining the distances of the sun, moon, and planets (N. 128). When the moon is in the horizon at the instant of rising or setting, suppose lines to be drawn from her center to the spectator and to the center of the earth; these would form a right-angled triangle with the terrestrial radius, which is of a known length; and as the parallax or angle at the moon can be measured, all the angles and one side are given; whence the distance of the moon from the center of the earth may be computed. The parallax of an object may be found, if two observers under the same meridian, but at a very great distance from one another, observe its zenith distances on the same day at the time of its passage over the meridian. By such contemporaneous observations at the Cape of Good Hope and at Berlin, the mean horizontal parallax of the moon was found to be 3459", whence the mean distance of the moon is about sixty times the mean terrestrial radius, or 237,360 miles

nearly. Since the parallax is equal to the radius of the earth divided by the distance of the moon, it varies with the distance of the moon from the earth under the same parallel of latitude, and proves the ellipticity of the lunar orbit. When the moon is at her mean distance, it varies with the terrestrial radii, thus showing that the earth is not a sphere (N. 129).

Although the method described is sufficiently accurate for finding the parallax of an object as near as the moon, it will not answer for the sun, which is so remote that the smallest error in observation would lead to a false result. But that difficulty is obviated by the transits of Venus. When that planet is in her nodes (N. 130), or within 110 of them, that is, in, or nearly in, the plane of the ecliptic, she is occasionally seen to pass over the sun like a black spot. If we could imagine that the sun and Venus had no parallax, the line described by the planet on his disc, and the duration of the transit, would be the same to all the inhabitants of the earth. But as the semi-diameter of the earth has a sensible magnitude when viewed from the center of the sun, the line described by the planet in its passage over his disc appears to be nearer to his center, or farther from it, according to the position of the observer; so that the duration of the transit varies with the different points of the earth's surface at which it is observed (N. 131). This difference of time, being entirely the effect of parallax, furnishes the means of computing it from the known motions of the earth and Venus, by the same method as for the eclipses of the sun. In fact, the ratio of the distances of Venus and the sun from the earth at the time of the transit are known from the theory of their elliptical motion. Consequently the ratio of the parallaxes of these two bodies being inversely as their distances, is given; and as the transit gives the difference of the parallaxes, that of the sun is obtained. In 1769, the parallax of the sun was determined by observations of a transit of Venus made at Wardhus in Lapland, and at Otaheite in the South Sea. The latter observation was the object of Cook's first voyage. The transit lasted

about six hours at Otaheite, and the difference in duration at these two stations was eight minutes; whence

the sun's horizontal parallax was found to be 8"-72. But by other considerations it has been reduced by Professor Encke to 8"-5776; from which the mean distance of the sun appears to be about ninety-five millions of miles. This is confirmed by an inequality in the motion of the moon, which depends upon the parallax of the sun, and which, when compared with observation, gives 8"-6 for the sun's parallax.

The parallax of Venus is determined by her transits; that of Mars by direct observation, and it is found to be nearly double that of the sun, when the planet is in opposition. The distance of these two planets from the earth is therefore known in terrestrial radii, consequently their mean distances from the sun may be computed; and as the ratios of the distances of the planets from the sun are known by Kepler's law, of the squares of the periodic times of any two planets being as the cubes of their mean distances from the sun, their absolute distances in miles are easily found (N. 132). This law is very remarkable, in thus uniting all the bodies of the system, and extending to the satellites as well as the planets.

Far as the earth seems to be from the sun, Uranus is no less than nineteen times farther. Situate on the verge of the system, the sun must appear to it not much larger than Venus does to us. The earth cannot even be visible as a telescopic object to a body so remote. Yet man, the inhabitant of the earth, soars beyond the vast dimensions of the system to which his planet belongs, and assumes the diameter of its orbit as the base of a triangle whose apex extends to the

stars.

Sublime as the idea is, this assumption proves ineffectual, except in a very few cases; for the apparent places of the fixed stars are not sensibly changed by the earth's annual revolution. With the aid derived from the refinements of modern astronomy, and of the most perfect instruments, a sensible parallax has been detected only in a very few of these remote suns. a Centauri has a parallax of one second of space, therefore it is the nearest known star, and yet it is more than two hundred thousand times farther from us than the sun

is. At such a distance not only the terrestrial orbit shrinks to a point, but the whole solar system, seen in the focus of the most powerful telescope, might be eclipsed by the thickness of a spider's thread. Light, flying at the rate of 190,000 miles in a second, would take more than three years to travel over that space. One of the nearest stars may therefore have been kindled or extinguished more than three years, before we could have been aware of so mighty an event. But this 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 depths 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 remote companion."

SECTION VIII.

Masses of Planets that have no Satellites determined from their Perturbations-Masses of the others obtained from the Motions of their Satellites -Masses of the Sun, the Earth, of Jupiter, and of the Jovial SystemMass of the Moon-Real Diameters of Planets, how obtained-Size of Sun-Densities of the Heavenly Bodies-Formation of Astronomical Tables-Requisite Data and Means of obtaining them.

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. The masses of the satellites themselves may also be compared with that of the sun by their perturbations. Thus, it is found, from the comparison of a vast number of observations, with La Place's theory of Jupiter's satellites,

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that the mass of the sun is no less than 65,000,000 times greater than the least of these moons. 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 (N. 133), 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 354,936 times that of the earth; whence the great perturbations of the moon, and the rapid motion of the perigee and nodes of her orbit (N. 134). Even Jupiter, the largest of the planets, has recently been found by Professor Airy to be 1048-7 times less than the sun; and, indeed, the mass of the whole Jovial System is not more than the 1046.77th part of that of the sun. So that the mass of the satellites bears a very small proportion to that of their primary. 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 74., 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 part of that of the earth-a value that cannot differ much from the truth.

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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 7916 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. According to Professor Bessel, the mean apparent diameter of the sun is 1922", and with the solar parallax 8"-5776, it will be found that the diameter of

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