hours. Let S be the sun, and R a fixed star, at such an immense distance, that the diameter GC of the earth's orbit, bears no sensible proportion to that distance; Nmn the earth in different points of its orbit. Let Nm be any particular meridian of the earth, and N a given point, or place, lying under that meridian.

When the earth is at A, the sun S hides the star R, which would always be hid if the earth never moved from A; and, consequently, as the earth turns round its axis, the point N would always come round to the sun and the star at the same time.

But when the earth has advanced through an eighth part of its orbit, or from A to B, its motion' round its axis will bring the point N an eighth part of a day, or three hours, sooner to the star than to the sun. For the star will come to the meridian in the same time, as though the earth had continued in its former situation at A; but the point N must revolve from N to n, before it can have the sun upon its meridian. The arc Nn being, therefore, the same part of a whole circle as the arc AB, it is plain that any star which comes to the meridian at noon, with the sun, when the earth is at A, will come to it at nine o'clock in the forenoon, when the earth is at B.

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When the earth has passed from A to C, onefourth part of its orbit, the point N will have the star upon its meridian, or at six in the morning, six hours sooner than it comes round to the sun; but the point N must revolve six hours more before it

has mid-day by the sun: for now the angle ASC is a right-angle, and so is NCn; that is, the earth has advanced 90 degrees on its axis, to carry the point N from the star to the sun; for the star always comes to the meridian, when Nm is parallel to RSA; because CS is but a point in respect to RS. When the earth is at D, the star comes to the meridian at three in the morning; at E, the earth having gone half round its orbit, N points to the star at midnight, it being then directly opposite to the sun; and, therefore, by the earth's diurnal'motion, the star comes to the meridian twelve hours before the sun, and then goes on, till at A it comes to the meridian with the sun again.

Thus it is plain, that one absolute revolution of the earth on its axis (which is always completed when any particular star comes to be parallel to its situation at any time of the day before), never brings the same meridian round from the sun to the sun again; but that the earth requires as much more than one turn on its axis, to finish a natural day, as it has gone forward in that time; which, at a mean state, is a 365th part of a circle.

From hence we obtain a method of knowing by the stars, whether a clock goes true or not. For if, through a small hole in the window-shutter, or in a thin plate of metal fixed to a window, we observe at what time any star disappears behind a chimney, or corner of a house, at a little distance; and if the same star disappears the next night, 3 minutes, 56 seconds, sooner by the clock; and on the second,

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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 proper 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, A B C D 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 PA, 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 S T, 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