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round the earth, in the time of one complete rotation, or in 23 hours, 56 minutes; which is the case with any of the fixed stars, and is therefore the length of a siderial day. But the sun is found to take up a longer time to complete its apparent revolution; for if it is in the south of any particular place at twelve o'clock at noon to-day, it will not complete an apparent revolution, so as to return to the south of that place again, till twelve o'clock at noon on the next day; and, consequently, the time of this apparent revolution is twenty-four hours.

Let us endeavour to render this subject clearer, by defining, in other words, the nature of the solar and siderial day.

The solar day is that space of time which intervenes between the sun's departing from any one meridian, and its return to the same circle again; which space is also called a natural day; or it is the time from the noon of one day to the noon of the next.

The siderial day is the space of time which happens between the departure of a star from, and its return to, the same meridian again.

I am now to shew why these days differ in length, or why the time, that the sun takes up to complete one revolution, is longer than the time the earth takes to revolve once upon its axis.

This difference arises from the sun's annual motion. For the sun does not continue always in the same place in the heaven, as the fixed stars do; but it is seen at M, plate 4, fig. 2, one day, near the fixed star R; it will have shifted its place the next

day, and will be near to some other fixed star L. This motion of the sun is from west to east, and one entire revolution is completed in a year. Suppose, therefore, that the sun, when it is at M, near to the fixed star R, appears in the south of any particular place S; and then imagine the earth to turn once round upon its axis from west to east, or in the direction of STVW, so that the place may be returned to the same situation; after this rotation is completed, the star R will be in the south of the place as before; but the sun having, in the meantime, moved eastwards, and being near to the star L, or to the east of R, will not be in the south of the place S, but to the eastward of it: upon this account, the place S must move on a little farther, and must come to T before it will be even with the sun again, or before the sun will appear exactly in the south.

This may be illustrated by an instance. The two hands of a watch are close together, or even with one another at twelve; they both turn round the same way, but the minute-hand turns round in a shorter time than the hour-hand; when the minute-hand has completed one rotation, and is come round to twelve, the hour-hand will be before it, or will be at one; so that the minute-hand must move more than once round, in order to overtake the hour-hand, and be even with it again.

As this subject is of some importance, we shall endeavour to render it more clear, by placing it in a different point of view: the more so, as it may ac custom the young pupil to reason on both hypotheses,

namely, the motion of the sun, and that of the earth.

The diameter of the earth's orbit is but a physical point, in proportion to the distance of the stars; for which reason, and the earth's uniform motion on its axis, any given meridian will revolve from any star to the same star again, in every absolute turn of the earth upon its axis; without the least perceptible difference of time being shewn by a clock which exactly true.

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If the earth had only a diurnal, without an annual motion, any given meridian would revolve from the sun to the sun again, in the same quantity of time as from any star to the same star again; because the sun would never change his place with respect to the stars. But, as the earth advances almost a degree eastward in its orbit, in the time that it turns eastward round its axis, whatever star passes over the meridian on any day with the sun, will pass over the same meridian on the next day, when the sun is almost a degree short of it; that is, 3 minutes, 56 seconds sooner. If the year contained only 360 days, the sun's apparent place, so far as his motion is equable, would change a degree every day; and then the siderial days would be just four minutes shorter than the solar.

Let ABCDEFGH, plate 4, fig. 3, be the earth's orbit, in which it goes round the sun every year, according to the order of the letters; that is, from west to east; and turns round its axis the same way, from the sun to the sun again, in every twenty-four

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.

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."

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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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