tangent to the orbit of the Earth, is greater than when E is at any other point, and therefore the planet being in quadrature, the exterior angle is least. SDE for every superior planet is acute, and the exterior angle obtuse, and consequently its versed sine is greater than radius. Whence more than half the disc of a superior planet is always seen, and it appears most gibbous in quadrature. Mars then appears gibbous about of his diameter; Jupiter only by about of his diameter, which quantity is imperceptible, even by a telescope, because Jupiter's disc then subtends only an angle of 30". Accordingly all the superior planets, except Mars, appear always with a full face.

The new planets appear so small, that it cannot be expected any gibbosity should be exhibited by them.

13. Mercury and Venus have the same phases from their inferior to their superior conjunction, as the Moon has from the new to the full; and the same from the superior to the inferior conjunction, as the Moon has from the full to the new.

Illustration. Let DabGON, (see fig. 1, page 258) be the orbit of Venus, ELT that of the Earth, and S the Sun; let E be the place of the Earth, when Venus is at a in her inferior conjunction with the Sun: the dark side of Venus is entirely turned towards the Earth, and she quite disappears, unless she happen to be in or near one of her nodes, when she will appear like a black spot, as has already been observed, or pass over the body of the Sun, and is then said to transit his disc. In passing from inferior conjunction to quadrature, less than half her enlightened face would be directed towards the Earth, and Venus would appear horned; at her quadrature, the part enlightened is 90 degrees; then the circle dividing the illuminated from the darkened hemisphere will be projected into a straight line, and half her disc will be seen. Between the quadrature and superior conjunction, more than half her enlightened hemisphere would be directed towards the Earth; for instance, if Venus were at O, and the Earth at E, then the circle dividing the illuminated from the darker part will be projected in an arc of an ellipse upon the disc, when the planet will appear gibbous. Let E be the place of the Earth, when Venus is at N in her superior conjunction with the Sun: the illuminated part of Venus is then directed towards the Earth, and, of course, the planet appears as a full lucid circle, like the Moon at full. In a similar manner

the appearances in the different positions from the superior to the inferior conjunction might be traced out; and the same delineation and explanation will serve for the planet Mercury.

14. The brightness of a planet depends both on the quantity of illuminated surface and its distance. The greater the distance is, the less the brightness; which, the illuminated surface remaining the same, decreases as the square of the distance increases, so thatin computing when a planet appears brightest, both the illuminated surface and distance must be taken into the account. Both circumstances concur in making a superior planet appear brightest at opposition. The inferior planets are not brightest at superior conjunction, because of their greater distance; and near inferior conjunction, the illuminated part visible to us is very small. The place of greatest brightness then lies between inferior and superior conjunction.

The solution of the problem when Venus appears brightest, gives her elongation then about 40 degrees. The places of greatest brightness are between the places of greatest elongation and inferior conjunction. This, according to Dr. Brinkley, agrees very well with observation. When she is near this position she occasions a strong shadow in the absence of the Sun; and for a considerable time both before and after she is at this elongation, she may be readily seen in full day-light by the naked eye.

QUESTIONS.

What is said of the planetary motions?

What is the greatest elongation of Mercury ? What of Venus?

Is an inferior planet direct or retrograde whilst passing between the Earth and Sun?

When is a superior planet retrograde, &c. ?

When is the direct motion of a superior planet the greatest?

When is the retrogradation of a planet the

greatest?

Is the mean arc of retrogradation of Mars greater than that of either of the other superior planets ? Do the phases of the inferior planets undergo the same changes as those of the Moon?

When does an inferior planet appear as a dark spot on the surface of the Sun ?

What is the reason Venus appears so much brighter when crescent, or between inferior and superior conjunctions, than when her illuminated disc is wholly turned towards the Earth?

CHAPTER V.

Of Mercury.

1. Mercury, the nearest planet to the Sun, performs its sidereal revolution round that body in 87 days, 23 hours, 15 minutes, and 44 seconds, which is the length of its year: the rotation of Mercury on its axis from west to east, or in the same direction as the Earth's diurnal motion, is performed in 24 hours, 5 minutės, and 28 seconds; which is the length of its day.

The interval of time which any planet employs in passing from a fixed star, or from one of the nodes, (making allowance for the secular variation of the node,) till it returns to the same again, is called the sidereal revclution of that planet. The time between two consecutive conjunctions, or oppositions, of a body with the Sun, is called a synodic revolution of that body.

The sidereal revolution of a planet round the Sun is usually called the length of that planet's year; and the time it takes to revolve on its axis, is the length of its day.

2. Mercury is a spherical body, whose diameter is about 3130 miles; its size is, therefore, nearly one sixteenth of that of the Earth; and its relative mean distance from the Sun is nearly 4, that of the Earth being considered as 10.

The magnitude or size of Mercury, according to Francœur, is .0565; its mass 1627, and its density 2.879646; the size, mass, and density of the Earth being respectively considered as unity, or 1. And a body weighing 1 pound on the surface of the Earth, will weigh 1 pound 8 drachms on the surface of Mercury.

Mercury is the smallest of all the principal planets, and moves the quickest in its orbit, its mean hourly motion being about 109,442 miles. Hence, it was that the Greeks gave this planet its name after the nimble messenger of the gods, and represented it by the figure of a youth with wings at his dead and feet; whence is derived, the character by which it is commonly represented.

3. The inclination of the orbit of this planet to the plane of the ecliptic, is the greatest of all the planets, except the four asteroids, being about 7°, which is equal to its greatest heliocentric latitude; and its orbit is also far more eccentric than that of any of the other planets, being about of its mean distance from the Sun.

The inclination of its orbit is subject to a small increase of about 18" in a century. The greatest geocentric latitude of this planet is about 4° 30'. Its greatest heliocentric latitude, in the present year, will take place place on or about the following days: January 19th, March 16th, April 19th, June 10th, July 16th, &c.

4. The extent, or angular distance, of the greatest elongations of Mercury from the Sun, on each side, varies from 16 degrees 42 minutes, to 28 degrees 48 minutes.

Mercury emits a very bright white light, but it is seldom to be seen, owing to its being so near the Sun; and when it makes its appearance, its daily mean motion is so swift, that it can be discerned only during a few successive evenings or mornings. For when it begins to appear in the evening, it is with difficulty distinguished in the rays of twilight: it disengages itself more and more in the following days, and after arriving at about 220 46' from the Sun, it returns towards him again. In this interval the motion of Mercury, with respect to the fixed stars, is direct; but when in returning it comes within the distance of 18 degrees of the Sun, it seems stationary, after which its motion appears retrograde, ret it continues to approach the Sun, and is again in the evening lost in his rays. After continuing some time invisible, it is seen again in the morning, disengaging itself from the Sun's rays and departing from the Sun, its motion is still retrograde as before its disapparition. Arrived at the distance of 18° it is again stationary, then resumes its direct motion, its distance increases to 220 30', it then returns, and disappearing in the morning in the light of the dawn, is soon after seen again in the evening, producing the same phenomenon as before.

5. The length of this planet's entire oscillation, or return to the same position relatively to the Sun, varies likewise from 106 to 130 days; the mean arch of retrogradation is about 13° 30', and its mean duration 23 days; but there is a great difference in their quantities in different retrogradations.

A long series of observations was no doubt necessary to recognise the identity of the two stars, which were alternately seen in the morning and in the evening to depart from and return to the Sun; but as one nevér showed itself till the other disappeared, it was at last suspected to be the same planet which thus oscillated on each side of the Sun. See La Place's System of the World.

6. The apparent diameter of Mercury is very variable, and its changes are evidently connected with its relative position to the Sun and the direc tion of his motion. The mean apparent diameter of this planet is about 7", and the greatest diamefor 11".