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Excepting the rotation of the Earth upon its axis, there is, as far as we know, no other body in nature, with which we are acquainted, whose motion is perfectly uniform and regular. The apparent motion of the Sun is very unequal, and therefore equal or true time, which flows on for ever in the same manner, cannot be truly measured by the Sun's apparent motion. Equal and true time is that which is shown by a well-regulated time-keeper, as a clock or watch; and in order that the apparent time, shewn by the sun-dial, may be made to agree with this, it must be corrected by proper equations, such as we have given in each of our astronomical portions, and an account of which we shall now endeavour to explain.

The difference between mean and apparent time depends chiefly on two causes, viz. 1. The obliquity of the ecliptic with respect to the equator; and, 2. The unequal motion of the Earth in its elliptical orbit. Since the Earth’s axis is perpendicular to the plane of the equator, any equal portions of the equator will, by means of the Earth's rotation upon its axis, pass over the meridian in equal times; and so, of course, would any equal portions of the ecliptic, provided it were parallel to, or coincident with, the equator. But as this is not the case, the daily motion of the Earth upon its axis will carry unequal portions of the ecliptic over

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the meridian in equal times, the difference being always in proportion to the obliquity : and, as some parts of the ecliptic are much more obliquely situated, with respect to the equator, than others; these differences will, therefore, be unequal among themselves. If, for instance, two bodies, the Sun and a star, were to set out together from one of the equinoctial points, and to move through equal spaces in equal times, the Sun in the ecliptic, and the star in the equator ; then the star moving in the equator would always return to the meridian exactly at the end of every twenty-four hours, as measured by a well-regulated clock; but the Sun moving in the ecliptic would come to the meridian sometimes sooner than the star, and sometimes not so soon, according to their relative situations; and they would never be found upon that circle exactly together, but on four days in the year, viz. on or about the 20th March and the 23d of September, when the Sun enters the equinoctial points; and on the list of June and the 21st of December, when that body is in the solstitial points.

This is easily shown on the globe, by making marks of chalk, or placing patches of black court-plaster, at equal distances, all round the globe, say 10 degrees, from each other ; beginning from the first of Aries, which answers to the 20th of March. Now, by turning the globe on its axis, it will be seen that all the patches in the first quadrant of the ecliptic, that is, from Aries to Cancer, come sooner to the brazen meridian than their corresponding marks on the equator. Hence, apparent time marked by the dial would be before equal or true time, and we should have to subtract to obtain the true equation. In the sécond quadrant, from Cancer to Libra, the patches in the ecliptic would come to the meridian later than those on the equator, and apparent time would be later than equal time, and we should have to add. In the other quadrants, the circumstances would be the same,

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that is, from Libra to Capricorn, the Sun would be soonest, and from Capricorn to Aries, it would be latest.

If, however, the reader refers to the tables of equation of time, in each month, they will be found not to answer exactly to this : the apparent motion of the Sun, or apparent time, does not begin to get before time by the clock till about the 16th of April, instead of the 20th of March ; and a similar change occurs about the 1st of September, instead of the 23d; and the times when the clock begins to surpass the Sun, are about the 16th of June and the 25th of December, instead of the 21st of June and the 21st of December, This is owing to the elliptical form of the Earth's orbit. If this orbit were circular, then the whole difference between equal time, as shown by the clock, and apparent, as shown by the dial, would arise entirely from the inclination of the Earth's axis; and the change from slow to fast, and fast to slow, would be, as we first mentioned, on the 20th of March, the 21st of June, the 23d of September, and the 21st of December.

This, however, is not the case; for the Earth travels when it is nearest the Sun, that is, in winter, more than a degree in twenty-four hours; and when it is farthest from the Sun, that is, in summer, less than a degree in the same time

; consequently, from this cause, if it were to act alone, the natural day would be of the greatest length when the Earth was nearest the Sun; for it must continue turning the longest time after an entire rotation, in order to bring the meridian of any place to the Sun again, and the shortest day would be when the Earth moves the slowest in her orbit. Now these inequalities, combined with those arising from the inclination of the Earth's axis to the ecliptic, or orbit of the Earth, make up that difference which is shown by the equațion table. In other words, the obliquity of the Earth's orbit to the equator on the Earth, which is the first-mentioned cause of difference between equal and apparent time, would

make the clock and dial agree when the Earth enters Libra, Capricorn, Aries, and Cancer; but the unequal motion of the Earth, in its orbit, would make them agree twice a year, when the Earth is in its aphelion and perihelion; and, consequently, when these two points fall in the beginning of Cancer and Capricorn, or of Aries and Libra, they will concur in making the Sun and clocks agree. But the aphelion is somewhere in the ninth degree of Cancer, and the perihelion in the ninth degree of Capricorn; and therefore the Sun and clocks cannot be equal about the beginning of those signs, nor at any time in the year, except when the swiftness or slowness of equation, resulting from one of these causes, just balances the slowness or swiftness arising from the other.

The times of Sun-rising and setting for the 1st, 11th, and 21st, will be found as follows, viz:

1st. Sun rises 35m. past 6. Sun sets 25m. past 5.
ilth.
15m. 6.

45m. 5.

21st.

55m.

5.

5m.

6.

Equation of Time.[See the month of January.]

The following table will show what is to be added to the apparent time shown on the dial, to obtain equal or true time for every 5th day of March. Tuesday, Mar. 1, to the time on the dial add 12m. 43s.? Sunday,

11 37 Friday,

10 21 Wednesday, 16,

8 57 Monday, 21,

7 28 Saturday, 26,

5 56

69

11,

To obtain true time by the clock.

The Georgian planet will be stationary on the 6th. The Sun enters the sign Aries, 37m. after 5 in the morning of the 21st. The planet Mercury will be found stationary on the 23d.

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