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as to us. The astonishing heat that it must have received from the sun in its perihelion, Sir Isaac New ton calculates to be 20,000 times the heat of red hot iron. And the distance to which it goes from the sun suggests to us an idea of the inconceivable distance of the fixed stars; as even at its greatest excursion it must still be nearer to the sun than to the nearest of the fixed stars, of whose attraction it must keep clear, in order to return periodically round the sun.

THE TRUTH OF THE COPERNICAN SYSTEM.

In the foregoing description of the solar system, we have taken notice of the phenomena that have been observed to take place among the heavenly bodies. We now assert farther, that these are just such as they ought to be, upon the supposition that the copernican system is true; and that they are inconsistent with either the tychonic or ptolemean hypotheses. The orbits of the inferior planets encompass the sun, but the earth is placed on the outside of these orbits, and consequently the ptolemean system is false, as it supposes the earth to be the center of their motions, and that their orbits are included by the orbit of the sun. And these planets are found on all sides of the sun, both east and west of him, as well as beyond him and between him and us: therefore they must surround the sun, and the earth be without of their orbits, according to the copernican system. Besides, if the orbits of the inferior planets surrounded the earth, they would sometimes be found in opposition to the sun, though they never are seen in opposition to him, but have two conjunctions with him in every revolution. Mercury is never seen above 23 degrees from the sun, and Venus not more than about 48 degrees. These things

are necessary consequences of the copernican syster, but impossible upon the ptolemean hypothesis. Besides, their apparent diameters increase and diminish by turns, as they should do upon the copernican hypothesis, whereas they should never vary by the ptolemean. In a word, their stations on each side of the sun, their direct and retrograde motions, their transits over the sun's disk, and their different phases of illumination, are such as they should be in the copernican system, but impossible in the ptolemean.

The earth is not at rest within the orbits of the superior planets, as is supposed both in the tychonic and ptolemean systems; for upon this supposition, the superior planets could never appear stationary or retrograde in their motions; but according to the copernican system, they ought to appear stationary, direct, and retrograde, exactly in the places where they are actually found to be so. As the phenomena of the heavenly motions are inexplicable by, and inconsistent with, the schemes of either Ptolemy or Tycho Brachè, they must be erroneous; and as the copernican system solves every phenomenon without exception, there can be no solid objection brought against it; and it should therefore be accounted true. Especially, when we add, the grand newtonian argument for the truth of the copernican system; that all the various combinations of their motions are the direct result of the single principle of gravitation, which pervades the whole system, and regulates all the complicated motions of both planets and comets, in all their different orbits. This force is directly proportional to the quantity of matter in the revolving bodies, and inversely as the squares of their distances from each other; from whence it follows, that the squares of their periodical times are

as the cubes of their mean distances from the common center of gravity: and every one of them describes equal areas in equal times. The moon is retained in her orbit, by the same force, that causes a heavy body here to descend 16 feet in a second of time. The moons of Jupiter and Saturn revolve round their primaries, by this law, and all the planets and comets revolve round the sun by the same. But if the sun and moon be supposed to revolve round the earth by this law, the sun's period would be no less than 475 years!

DISTANCES AND PARALLAXES OF THE PLANETS.

THE distances of the planets from the sun are found by means of their parallaxes.

The parallax of a heavenly body is the difference between the places, among the stars, in which it would be seen by a spectator at the center, and at the surface of the earth. Consequently it is the measure of the angle under which the semidiameter of the earth is seen, from the heavenly body. Therefore, as a spectator at the center of the earth would see an object in the same place in the heavens, as a spectator on its surface would see it, when in his zenith, the parallax of any object in the zenith is nothing, and it gradually increases with its distance from the zenith until it appear in the horizon, when it will be greatest. So that the horizontal parallax is the greatest, and the parallax at any other altitude is as the cosine of the altitude, or sine of the zenith distance. As the true place of a planet is the place in which it would appear from the center of the earth, the apparent place, to which it is referred by a spectator on the surface of the earth, must always be lower than the true. As the parallactic angle of a celestial object is always sub

tended by the semidiameter of the earth, it must be less as the distance of the object from the earth increases. So that the distance of the heavenly bodies is inversely as their parallaxes. That is, the greater their parallax is, the less is their distance. The parallax of a planet at any altitude is to the semidiameter of the earth, as the sine of its zenith distance is to its distance from the center of the earth.

If we therefore could find the parallax of any planet, we could easily determine its distance from the earth, by the foregoing analogy. Or if we had the horizontal parallax of a planet, we could find its distance by this analogy: as the tangent of the horizontal parallax is to radius, so is the earth's semidiameter to the distance of the planet from the earth. Thus, if the sun's horizontal parallax be 8".65, as it was found to be at the late transit of Venus, we find his distance from us, by the preceding analogy, to be 95,173,117 miles.

As the periodical times of all the planets are known from observation, if the mean distance of any one of them be found by means of its parallax, the distances of all may be found by the proportion, before mentioned, between the mean distances and periods.

But the parallax of the planets and comets, on account of their great distance, is so small, that it cannot be directly observed with sufficient precision, for so nice an affair as the determination of their distances, as it amounts to a few seconds only; and an error of a single second, in observing the parallax, would produce an error of some millions of miles in the distance.

The most certain way of determining the parallax of the sun, is by observing that of Venus; because she is nearer to us than any of the planets in her inferior conjunction; and consequently she has a larger

parallax, and therefore it may be observed with greater precision. But Venus at that time is too near to the sun to be seen by us; as her enlightened disk is then turned from us, 'unless she should then be in or near to one of her nodes, when she would appear like a black spot on the face of the sun. These transits, from the laws of her motion, happen very seldom. Three only have been observed; and from the two last of them, in the years 1761, and 1769, the parallax of the sun has been calculated to be but 8".65. Dr. Halley first proposed this use of the transits of Venus, and they have been accordingly observed by the astronomers of the present day, with great diligence and success.

To give a general idea, how this important observation may be made, without entering into the minutiæ of calculation necessary in this nice affair, we shall just mention the outlines of the business.

Let ABD be the earth, V, Venus in her orbit, S the eastern limb of the sun, and FeE the sphere of the fixed stars. To a spectator at B, Venus appears just entered on the sun at S, and her place among the fixed stars is E; while to a spectator at A, her place among the stars is at F, and the arch FE, or angle FVE AVB is her horizontal parallax: but the arch Ee, or angle eSE=BSA is the horizontal parallax of the sun. The difference of these parallaxes is FE, or the angle VAv, called the parallax of Venus from the sun; and may be measured by the difference of time between the internal contact of the limbs of Venus and the sun, as observed at the places B and A, when the velocity of Venus in her orbit is previously known from the tables of her motion. Now in the triangle

* See Plate 15. Fig. 1.

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