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As viewed from the earth, Venus is the most brilliant of all the planets; and may sometimes be seen with the naked eye at noon day. She is known and recognised as the morning and evening star: and never recedes far from the sun. Her elongation, or angular distance, varies from 45° to 47°. 12'.

Her course sometimes appears retrograde. The arc, which she describes in such cases, varies from 14°. 35' to 17. 12' its duration, in the former case, is 40d. 21h, and in the latter case 43d. 12h. This retrogradation commences or finishes when she is at a distance from the sun, which varies from 27°. 40′ to 29°. 41′.

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Venus is sometimes seen to pass over the sun's disc which can happen only when she is in her nodes, and when the earth is in the same longitude. Consequently this phænomenon, for many centuries to come, can take place only in the months of June or December. It is a phænomenon indeed of very rare occurrence, as may be readily seen by the following list, which contains all those transits of Venus which have occurred since that which took place in December 1639 inclusive (the first that was ever known to have been seen by any human being) to the end of the 21st century.

1639 Dec. 4
1761 June 5

1769 June 3

1874 Dec. 8

* 1882 Dec. 6
* 2004 June 7

2012 June 5

THE EARTH.

THE earth which we inhabit is also one of the planets that revolve about the sun. Its mean distance from the sun is 23984 times its own semidiameter: whence it is nearly 95 millions of miles distant from that luminary. If this mean distance be assumed equal to unity, we shall have its distance at the perihelion equal to 9832; and its distance at the aphelion equal to 1.0168.

It performs its mean sidereal revolution in 365.2563612 mean solar days, or 365d. 6h.9m. 95,6: but the time employed in going from one equinox to the same again, or from one tropic to the same again (whence called the tropical revolution), is only 365-2422414 mean solar days, or 365d. 5h. 48m. 495,7*. The tropical year is about 45,21 shorter than it was at the time of Hipparchus.

Its mean longitude, at the commencement of the present century, was in 100°. 39′. 10",2: after subtracting 20" for the effect of aberration.

Its motion varies in different parts of its orbit. Like all the other planets, it is most rapid in its perihelion, and slowest in its aphelion. In the former point it describes an arc of 1°. 1'.9′′,9 in a mean solar day: and in the

* M. Lalande makes this equal to 48,0; whilst M. Delambre makes it 51,6. In fact, if we augment the duration of the year 15, we must diminish the secular motion of the sun 4", 1. See the note in page 3.

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latter point it describes an arc of only 57'. 11",5 in the same period. Its mean motion is 0°.98564722, 0°. 59'. 8",32999 in a mean solar day; and 0°.98295603, or 0°. 58'. 58",64172 in a sidereal day.

The mean longitude of its perihelion, at the commencement of the present century, was 99°. 30′. 5",0. But the line of the apsides has a motion, to the eastward, of 11",8 in a year: which line, being referred to the ecliptic, will (on account of the precession of the equinoxes) appear to have a motion of 61",9 in a year. M. Laplace prefers 61",76. A revolution of the earth, from one end of the apsides to the same point again, is called an anomalistic year: and, on the assumption of the quantity stated by M. Laplace, is performed in 365-2595981 mean solar days, or in 365d. 6h. 13m. 49,3. The perihelion coincided with the vernal equinox about the year 4089 before the Christian era: it coincided with the summer solstice about the year 1250 after Christ: and will coincide with the autumnal equinox about the year 6483. A complete tropical revolution of the apsides is performed in 20984 years.

The axis of the earth is inclined to the pole of the ecliptic in an angle which, at the commencement of the present century, was 23°. 27'. 56",5*: which angle is called the obliquity of the ecliptic. It is observed to decrease at the rate of 0",4755 in a year. But, this variation is confined within certain limits; and cannot exceed 2o. 42'. `

This angle is also subject to a periodical change called the nutation; depending principally on the place of the moon's node: whereby the axis of the earth appears to describe a small ellipse in the heavens. The semi major

* M. Bessel makes this only 54",32 with an annual diminution of 0',46.

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COS 2 w

COS W

axis of this ellipse is found by M. Laplace from theory to be 9",40: but Dr. Brinkley, from a comparison of numerous observations, makes it only 9",25. If a denote the semi axis major of this ellipse, the semi axis minor (b) will be b = xa: being the obliquity of the ecliptic. The sun has likewise an effect on the variation of this angle; which amounts, at a maximum, according M. Laplace from theory, to 0",493: but, according to Dr. Brinkley from observation, to 0",545. These variations in the obliquity of the ecliptic affect the right ascensions and declinations of the stars, according to their positions in the heavens.

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The intersection of the equator with the ecliptic is not always in the same point; but is constantly retrograding, or receding contrary to the order of the signs. Consequently the equinoctial points appear to move forward on the ecliptic: and whence this phænomenon is called the precession of the equinoxes. The quantity of this annual change caused by the action of the sun and moon, and which is called the luni-solar precession, is 50",41; from which we must deduct the direct motion caused by the planets, equal to 0",31: and the difference, or 50",10 is the general precession in longitude. It is subject to a small secular variation. A complete revolution of the equinoxes is performed in 25868 years.

This precession is also subject to a periodical change, caused by the nutation of the earth's axis; and which affects the right ascensions of all the stars, by quantities depending (like the nutation of the obliquity) on the mean place of the moon's node and on the true longitude of the sun. M. Laplace's theory makes the constant of lunar nutation in longitude equal to 17",579; and of the solar

nutation equal to 1",137. But Dr. Brinkley makes the former 17"299; and the latter 1",255.

The eccentricity of the orbit of the earth is 0.016783568; half the major axis being considered as unity *. The major axis therefore will be to the minor axis of the orbit, as 1 to 99986. The eccentricity of the earth's orbit is subject to a decrease of 0.00004163 in a century.

The sidereal day, or the time employed by the earth in revolving on its axis from any given star to the same star again, is always the same: and has not varied 0$,003 since the time of Hipparchus. It is divided into 24 sidereal hours; and these are again subdivided into sidereal minutes and seconds. This mode of reckoning time, during the day, is now universally adopted by astronomers in their observatories: although the commencement of the day is still determined by the apparent culmination of the sun.

A mean solar day, as adopted by the public in this country, is the time employed by the earth in revolving on its axis, as compared with the sun, supposed to move at a mean rate in its orbit, and to make 365-2425 revolutions in a mean Gregorian year. But the mean solar day, adopted by astronomers, is founded on the assumption that the sun makes only 365-2422414 revolutions in a mean Gregorian year. It is divided into 24 mean solar hours; and these are again subdivided into mean solar minutes and seconds.

If the sidereal day be taken equal to 24 sidereal hours,

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48

*M. Laplace makes this equal to 01685318, which appears to be E 11 E3 too great. The present value is deduced from the formula where E denotes the greatest equation of the centre, and which I have assumed equal to 10.55'.27",3.

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