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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. 285 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, it furnishes a standard of measure with which the dimensions of the solar system may be compared.
The parallax of a celestial body is the angle under which the radius of the earth would be seen if viewed from the centre of that body; it affords the means of ascertaining the distances of the sun, moon, and planets. Suppose, when the moon is in the horizon at the instant of rising or setting, lines to be drawn from her centre to the spectator and to the centre 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 centre 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 distance 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 237360 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.
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, or within 14° 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 semidiameter of the earth has a sensible magnitude when viewed from the centre of the sun, the line described by the planet in its passage over his disc appears to be nearer to his centre, 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. 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 to 8":577; from which the mean distance of the sun appears to be about 92246700 miles, or ninety-two millions of miles nearly. 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 distances of these two planets from the earth are 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, their absolute distances in miles are easily found.
Far as the earth seems to be from the sun, it is near to him when compared with Uranus; that planet is no less than 1843000000 of miles from the luminary that warms and enlivens the world; 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, for the apparent places of the fixed stars are not sensibly changed by the earth's annual revolution; and with the aid derived from the refinements of modern astronomy, and of the most perfect of instruments, it is still a matter of doubt whether a sensible parallax has been detected even in the nearest of these remote suns. If a fixed star had the parallax of one second, its distance from the sun would be 20500000000000 of miles. 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 covered by the thickness of a spider's thread. Light flying at the rate of 200000 miles in a second, would take three years and seven days 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