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ameters Sir Isaac Newton fixes to be that of 230 to 229. And the measures that have been made of the length of different degrees of latitude in various parts of the earth, when compared with one another, have induced the astronomers of Europe to acquiesce in his determination, as being nearly a mean of all their measures. As the sun and moon are out of the plane of the equator, for the greatest part of the year, and attract this redundancy of matter, that is accumulated round the equator, more forcibly than the other parts of the earth, they must have a constant tendency to bring the equatorial parts of the earth directly under them. The consequence of this must be, that the equator will be brought under the sun, before an annual revolution is completed, as counted from the time when the sun was at the same equinox before; or in less time than is necessary for a complete revolution of the earth round the sun, by 20′ 17′′ of time. So that from the time the sun is in the equator at the vernal equinox, till his return to it again, there will elapse only 365 5h 48′ 57′′; whereas the periodical time of the earth is 365d 6h 9' 14". The first of these intervals of time is called the tropical year, the other is called the sidereal. In the difference of these times, viz. 20′ 17′′, the sun comprises an arch of 50" of a degree: so that after he has left the equator, at an equinox, he crosses it again while he is 50" of a degree to the westward of the point where he crossed it before. Hence the equinoctial points shift backwards, or to the westward, at the rate of 50" per annum, or a degree in 72 years. This is called the precession of the equinoxes. This point of intersection, where the ecliptic cuts the equator, however it be continually shifting towards the west, is still called the first point or beginning of Aries, without any regard to the stars of

that constellation. This retrocession of the equinoxes towards the west has occasioned a small apparent motion of all the fixed stars towards the east, at the rate of a degree in 72 years. So that those stars, which were in the infancy of astronomy in the sign Aries, are now advanced into the sign Taurus, and those of Taurus are now in the sign Gemini. At the creation of the world, the star that was at the intersection of the equator and ecliptic, in 5790 years will, at the rate of 50" per annum, have advanced 2° 20′ 25′′ towards the east; and after 25920 years the intersection will have receded quite round the equator. The consequence of this motion is, that the pole of the earth's axis would describe a circle round the pole of the ecliptic, in 25920 years, denominated the great year, keeping at the same distance of 23° 28' from it, if the obliquity of these circles continued the same. But it will gradually approach towards the pole of the ecliptic in each revolution, at the rate of about half a second per annum, or 3° 36′ in each revolution: and by the same quantity does the obliquity of the ecliptic to the equator decrease. It is now about a third part of a degree less than what it was in the time of Ptolemy, and most of the astronomers since his time have found it to decrease gradually down to the present time. This arises from the same cause with the precession of the equinoxes. Because the sun and moon acting, for the most part, obliquely, on the redundancy of matter about the equator, must necessarily bring these circles to a nearer coincidence with each other.*

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* It has been satisfactorily demonstrated by M. le Grange, that the ecliptic will never coincide with the equator, nor change its inclination above 2 degrees; but that the solar planetary system oscillates, as it were, round a medium state, from which it will never swerve very far.

Ed.

EQUATION OF TIME.

FROM the obliquity of the ecliptic to the equator, and the unequal motion of the earth in her elliptical orbit, there arises an inequality in the lengths of days as measured by the returns of a star and of the sun to any given meridian; which is called the equation of time. As the earth's motion on her axis is perfectly equable, never going faster at one time than at another, the sidereal days are all equal, and so would the solar days also be, if the sun always appeared to move in the equator, and the earth's orbit were a perfect circle, so that the sun would appear to advance to the eastward of a given star an equal space daily. But this not being the case, his motion is very unequal, and he sometimes appears to revolve round in less than 24 hours, and at other times he requires more time to reach the same meridian which he left, on the preceding noon. The time shown by the sun is measured by a sun dial, but the time shown by the stars is measured by a clock, which goes regularly. The dial and the clock therefore can never agree together excepting on four days of the year. The clock will be before the dial, from the 24th of December till the 15th of April, and from the 16th of June till the 31st of August; and behind it, at all other times. The difference between the clock and the dial will amount to about a quarter of an hour, when greatest, and will gradually decrease and diminish down to nothing on these four days. As this difference arises from two causes, first, the obliquity of the ecliptic to the equator, and secondly, the unequal apparent motion of the sun in his elliptical orbit, we must consider each of these causes separately, and then determine their joint effect.

As the solar day is longer than the sidereal day, any point on the surface of the earth describes more than a whole circle in the course of a solar day, seeing the sun in the mean time has advanced about a degree to the eastward. This arch which the place describes, more than a complete circle in a solar day, is equal to the sun's daily increment of right ascension. Now these daily increments of A. R. would be different on account of the obliquity of the ecliptic to the equator, even although the sun's motion in the ecliptic were uniform. For if the sun advanced an equal space daily along the ecliptic, yet as this space has very different positions with respect to the equator, being at the tropics parallel to it, and at other places oblique; it will require a greater or less additional turn of the earth on her axis over and above a complete rotation to bring the sun on the meridian; according as these spaces are less or more inclined to the equator. At the equinoxes and solstices, the right ascension and longitude of the sun are equal, but at all other times they are different; and therefore as the motion in right ascension, or on the equator, is measured by a well-regulated clock, while the motion in longitude or on the ecliptic is measured by a dial, the clock and dial cannot agree, except at the equinoxes and solsti. ces, when the sun's longitude and right ascension are equal; provided the whole equation depended upon this cause, viz. the obliquity of the ecliptic to the equator; as would be the case, if the apparent motion of the sun were equable in his apparent orbit.

But this is not the case; for part of the equation of time depends upon the sun's unequable motion in his apparent orbit. He sometimes moves more than a degree in a day, and sometimes less. His motion being quickest in winter, when he is nearest to us, and slow31

est in summer, when ne is at his greatest distance. His motion, as it is measured by the dial, is slower than his mean motion which is measured by the clock, while the upper half of the earth's orbit is described, and quicker, while the other half is passed over. While his anomaly, or mean motion counted from his apogee, is less than six signs or half a circle, he comes to the meridian before twelve by the clock, because his motion being then slower than the mean motion, his daily increment of right ascension is less, and therefore it requires but a small time for any meridian to come up to him. But while his anomaly is more than six signs, or a semicircle, he comes to the meridian after twelve by the clock, because he has gone farther towards to the east, by his quicker motion, and therefore it requires a longer time for any meridian to come under the sun, after a complete revolution of the earth round its axis. Now the first-mentioned cause of the equation of time making it vanish at the equinoxes and solstices, and the last-mentioned making it vanish at the apogee and perigee; it cannot vanish entirely at any of these times, but at the four intermediate times above-mentioned.

The time measured by the sun-dial is called apparent time, but that measured by the clock is called mean time: and the difference between these is the equation, which being sometimes added to, and sometimes subtracted from apparent time, will give the mean time.

The only difficulty now remaining is, how to find the quantity of this equation of time, and to know whether it be additive to mean time or subtractive from it, to give the true. This may be known in the following manner.

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