7 minutes, 52 seconds sooner; the third night, 11 minutes, 48 seconds sooner, and so on every night; it is an infallible sign that the machine goes true; otherwise it does not, and must be regulated accordingly. This method may be depended on to nearly half a second*.

AN EXPLANATION OF THE PHENOMENA WHICH ARISE FROM THE MOTION OF THE EARTH, AND OF THE INFERIOR PLANETS, MERCURY AND VENUS.

It will be necessary, in this place, to define more exactly some words which have been slightly explained before, and recal the reader's attention to some definitions that have been already given; and, it is presumed, that these repetitions will not be an object of complaint; because they will answer the beneficial purpose of grounding the reader more firmly in the knowledge of the science, to which this Essay is intended as an introduction.

When two planets are seen together in the same sign of the zodiac, and equally advanced therein, they are said to be in conjunction. But when they are in

* A telescopic tube, with intersected wires at the focus of the first eye-glass, fixed against a wall, or the telescope of a theodolite, or other instrument, when placed firmly on its stand, are preferable and more accurate instruments. When a telescope, on a pro per and firm stand, is placed duly in the meridian of the place for this purpose, it then becomes a meridian or transit telescope; and is the best instrument for adjusting and ascertaining the rate of clocks and chronometers. EDIT.

opposite signs of the zodiac, they are said to be in opposition. Thus a planet is said to be in opposition to the sun, when the earth is between the sun and the planet.

The elongation of a planet is its apparent distance from the sun. When a planet is in conjunction with the sun, it has no elongation; when in opposition its elongation is 180 degrees.

The nodes of a planet's orbit, are those two points where the orbit cuts the plane of the ecliptic. I before observed, that the orbits of all the planets are inclined to the plane of the ecliptic, and consequently cross this plane. In plate 3, fig.3, ABCD is the plane of the ecliptic; EBFD is the orbit of a planet, in which the points B and D are the two nodes.

The line of the nodes is a line BD, supposed to be drawn through the sun from one node to the other. The limits of a planet's orbit, are two points in the middle between the two nodes. The point E is called the greatest northern limit, F the greatest southern limit.

The greatest distance of the earth, or of any planet from the sun, is called its aphelion, or higher apsis; its least distance is called the perihelion, or lower apsis.

Thus in plate 3, fig. 4, A is the place of the aphelion, P that of the perihelion.

The axis P A, fig.4, of any planet's elipsis, is called the line of the apsides: the extreme points of its shortest diameter T V, are the places of its mean distance from the sun; and ST, or S V, the line of its mean distance.

When a planet moves according to the order of the signs, its motion is said to be direct, or in consequentia; but when its motion is contrary to the or der of the signs, it is said to be retrograde, or in antecedentia.

The place in the starry heavens that any planet appears in, when seen from the centre of the earth, is called its geocentric place. The place where it would be seen in the celestial sphere, by an observer supposed to be in the sun, is called its heliocentric place.

OF THE CONJUNCTIONS AND ELONGATIONS OF THE INFERIOR PLANETS, VENUS AND MERCURY.

There are two different situations, in which an inferior planet will appear in conjunction with the sun; one when the planet is between the sun and the earth, and the other when the sun is between the earth and the planet. Let A, plate 6, fig. 2, be the earth in its orbit, E the place of Venus in her orbit EHG, S the sun, FVPQRTD an arc in the starry heavens. In this situation the sun and Venus are on the same side of the earth, and will appear in the same point of the heavens, so as to be in conjunction. If the earth is at A, and Venus at G, they will also appear to be in conjunction.

If the earth is at A, the sun at S, the planet at E, nearer to the earth than the sun, it is called its inferior conjunction. But if the earth is at A, and the

planet at G, farther from the earth than the sun, this is called the superior conjunction of the planet.

If an inferior planet is at E, the earth at A, and the sun at S, the elongation is nothing, the planet being then in its inferior conjunction. As the planet moves from E to y, its elongation increases; for, when it is at y, it appears in the line AyP, while the sun appears in the line ASQ; so that PAQ will be its elongation. When the planet is arrived at æ, it appears in the line AxV, which is a tangent to its orbit; and then its elongation is VAQ, which is the greatest that can be on that side the sun; for, after this, the elongation decreases. When the planet is at K, its elongation is PAQ; when at G, it is nothing, because it is then in its superior conjunction ; as the planet moves on from G, its elongation again increases; for, when it comes to C, it appears in the line ACR, and its elongation is RAQ. When the planet comes to H, a line drawn from the earth through the planet, is a tangent to the orbit; and the elongation is TAQ, the greatest it can have when it is on the other side of the sun; for, after this, the elongation again decreases.

Hence it is clear, that the inferior planets can never appear far from the sun, but must always accompany it in its apparent motion through the ecliptic. When we see either Venus or Mercury, it is either in the evening in the west, soon after the sun has set; or, in a morning, a little before the sun rises. Venus is, indeed, bright enough sometimes to be seen in the day-time, but then she is never far from the

sun.

The greatest elongation of Venus is about 40, and of Mercury about 33 degrees.

If the earth is at A, plate 6, fig. 2, when Venus appears in any part of the arc ExG, she is westward from the sun; and, therefore, rises before him in the morning, and is called the morning star. When she appears any where in the arc GHE, she is eastward from the sun, and therefore sets after him; is seen in the evening, and is then the evening star.

From the apparent motions of the inferior planets, we derive an argument to prove the falsity of the Ptolemaic system. If the earth was within the orbit of Venus, as the Ptolemaic system supposes, she might be sometimes on one side of the earth, whilst the sun is on the opposite side; or Venus might be sometimes in opposition to the sun; but Venus is never seen in opposition. Therefore the earth is on the outside of the orbit of Venus; and, consequently, the Ptolemaic system is not true. The same is also true of Mercury. But this, and some other circumstances relative to the motions of these planets, will be much better understood by means of a planetarium than by a diagram.

OF THE RETROGRADE, DIRECT, AND STATIONARY MOTIONS, OF VENUS AND MERCURY.

It is easy to explain these motions on the Coper nican system, it being the natural result of the respective situations and motions of the earth and these