SECTION EIGHTH.

OF THE EQUATION OF TIME, AND PRECESSION OF THE EQUINOXES.

THE stars appear to go around the earth in 23 hours 56 minutes and 4 seconds, and the Sun in 24 hours. So that the stars gain 3 minutes and 56 seconds upon the Sun every day; which amounts to one diurnal revolution in a year, or 365 days, as measured by the returns of the Sun to the meridian; there are 366 days as measured by the stars returning to it. The former are called solar days; the latter sidereal.

The earth's motion on its axis being perfectly uniforın, and equal at all times of the year; the sidereal days are always precisely of an equal length, and so would the solar days be if the earth's orbit were a perfect circle, and its axis perpendicular to it. But the earth's diurnal motion on an inclined axis, and its annual motion in an elliptical orbit, cause the Sun's motion in the Heavens to be unequal; for sometimes he revolves from the meridian to the meridian again in somewhat less than 24 hours; shown by a well regulated clock, and at other times in somewhat more; so that the time shown by a true going clock, and true sun-dial is never the same; except on the 15th day of April, the 16th of June, the 31st of August, and the 24th day of December. The clock, if it goes equally true during the whole year, will be before the Sun from the 24th of December till the 15th of April; from that time till the 16th of June, the Sun will be faster than the clock.

Let S be the sun, (plate 5th fig. Sth) E the earth, AM P the earth's orbit, A the aphelion, P the perihelion, the line MS the mean proportional between the semi-axis of the orbit, M a point in the equator represented by the external circle of the earth E. Let the spaces AS a M S n PS p represent equal areas of the orbit. The arches of these by the great law of Kepler represent the earth's motion in equal times as a solar day. It is evident that the point m when the earth is at a, at n, or at p, must pass from m to the line ES to complete a solar day. It is also evident that it must pass farther when the earth is at p, than when it is at a; the distance at n being a mean between the extremes. A day therefore, measured by the Sun, will agree with that shown by a good timekeeper, when the earth is at M. At A it will be shorter, and at Plonger than the true day of the clock.

The point where the Sun is at his greatest distance from the earth is called the Sun's apogee. The point where he is at his least distance from the earth is called his perigee; and a straight line drawn through the earth's centre from one of those points to the other is called the line of the apsides.

The distance that the Sun has gone in any time from his apogee, is called his mean anomaly, and is reckoned in signs, degrees, minutes and seconds, allowing 30 degrees to a sign.

OF THE PRECESSION OF THE EQUINOXES.

It has been observed, that by the earth's motion on its axis, there is more matter accumulated around the equatorial parts than any where else on the surface of the earth. The Sun and Moon, by attracting this redundancy of matter, bring the equator sooner under them in every return towards it, than if there were no such accumulation. Therefore if the Sun sets out as from any star, or other fixed point in the Heavens, the moment when he is departing from the equinoctial, or from either tropic, he will come to the same equinox or tropic again 20 minutes and 17 seconds of time, or 50 seconds of a degree, before he completes his course so as to arrive at the same fixed star, or point from whence he set out. For the equinoctial points recede 50 seconds of a degree westward every year, contrary to the Sun's annual progressive motion.

When the Sun arrives at the same equinoctial,* or solstitial point, he finishes what is called the tropical year; which, by observation, is found to contain 365 days, 5 hours, 48 minutes, and 47 seconds, and when he arrives at the same fixed star again, as seen from the earth, he completes the sidereal year, which contains 365 days, 6 hours, 9 minutes, 14 and a half seconds.

The sidereal year is therefore 30 minutes 17 and a half seconds longer than the solar, or tropical year, and 9 minutes, 14 and a half seconds longer than the Julian or civil year, which we state at 365 days, 6 hours.

As the Sun describes the whole ecliptic, or 360 degrees in a tropical year, he moves 59 minutes, 8 seconds of a degree every day, at a mean rate; therefore he will arrive at the same equinox, or solstice, when he is 50 seconds of a degree short of the same star or fixed point in the Heavens, from which he set out in the year before. So that with respect to the fixed stars, the Sun and equinoctial points fall back 30 degrees in 2,160 years, which will make the stars appear to have gone 30 degrees forward with respect to the signs of the ecliptic in that space of time; for the same signs always keep in the same points of the ecliptic, without regard to the constellations.

The Julian year exceeds the solar by 11 minutes and 3 seconds, which in 1,438 years amount to eleven days, and so much our seasons had fallen back with respect to the days of the months since the time of the Nicene Council, in A. D. 325, and therefore to bring back all the feasts and festivals to the days then settled, it was requisite to suppress 11 nominal days. And that the same seasons might be kept to the same time of the year for the future, to leave out the bissextile day in February, at the end of every century, not divisible by four, reckoning them only common years, as the 17th, 18th, and 19th centuries; namely, the years 1700, 1800, and 1900, &c. because a day intercalated every fourth year was too much, and retaining the bissextile at the end of those centuries of years which are divisible by four, as the years 1600, 2000, 2400, &c. otherwise in length of time, the seasons would be quite reversed with regard to the months of the year; though it would have required near 23,783 years to have brought about such a total change. If the earth had exactly made 3654 diurnal revolutions on its axis, whilst it revolved from any equinoctial or solstitial point to the same again, the civil and solar years would always have kept pace together, and the style would never have needed any alteration.

INTERROGATIONS FOR SECTION EIGHTH.

In what time do the stars appear to go round the Earth?

In what time does the Sun appear to go round the

Earth?

In what time do the stars gain one revolution?

How many days in a solar year?

How many in a sidereal?

Is the motion of the earth on its own axis uniform at

all times of the year?

Are the sidereal days always of the same length ?

Is the Sun's apparent diameter in the Heavens always equal?

On what days of the year are the Sun and clock together?

Between what periods will the clock be before the Sun?

Between what periods will the Sun be before the clock?

What is called the Sun's apogee ?

What his perigee?

What the line of the Apsides ?

What is meant by the Sun's mean anomaly?

How is his mean anomaly reckoned?

What is meant by the precession of the equinoxes?
Is there more matter accumulated at the equator than

at any other part of the earth?

What is the cause of such accumulation?

What is the Equator?

What effect is produced by this accumulation of matter?

How many seconds of a degree do the equinoctial points recede westward every year?

What are meant by the equinoctial points?

What the solstitial?

Which is the longest, the sidereal or solar year, and how much?

How many degrees will the equinoctial points fall back in 2,160 years?

Do the same signs always keep in the same point of the ecliptic?

Which is the longest, the Julian or the solar year, and how much?

How many days' difference will this make in 1,433 years?

In what year of the Christian era was the Council of Nice held?

What centuries were to be leap years?

What is the difference between the old and new styles in the present century?