PRACTICE
, in Arithmetic, is a rule which expeditiously and compendiously answers questions in the golden rule, or rule-of-three, especially when the first term is 1. See rules for this purpose in all the books of practical arithmetic.
PRECESSION of the Equinoxes, is a very slowmotion of them, by which they change their place, going from east to west, or backward, in antecedentia, as astronomers call it, or contrary to the order of the signs.
From the late improvements in astronomy it appears, that the pole, the solstices, the equinoxes, and all the other points of the ecliptic, have a retrograde motion, and are constantly moving from east to west, or from Aries towards Pisces, &c; by means of which, the equinoctial points are carried farther and farther back, among the preceding signs or stars, at the rate of about 50″ 1/4 each year; which retrograde motion is called the Precession, Recession, or Retrocession of the Equinoxes.
Hence, as the stars remain immoveable, and the equinoxes go backward, the stars will seem to move more and more eastward with respect to them; for which reason the longitudes of all the stars, being reckoned from the first point of Aries, or the vernal equinox, are continually increasing.
From this <*>ause it is, that the constellations seem all to have changed the places assigned to them by the ancient astronomers. In the time of Hipparchus, and the oldest astronomers, the equinoctial points were <*>ixed to the first stars of Aries and Libra: but the signs do not now answer to the same points; and the stars which were then in conjunction with the sun when he was in the equinox, are now a whole sign, or 30 degrees, to the eastward of it: so, the first star of Aries is now in the portion of the ecliptic, called Taurus; and the stars of Taurus are now in Gemini; and those of Gemini in Cancer; and so on.
This seeming change of place in the stars was first observed by Hipparchus of Rhodes, who, 128 years before Christ, found that the longitudes of the stars in his time were greater than they had been before observed by Tymochares, and than they were in the sphere of Eudoxus, who wrote 380 years before Christ. Ptolomy also perceived the gradual change in the longitudes of the stars; but he stated the quantity at too little, making it but 1° in 100 years, which is at the rate of only 36″ per year. Y-hang, a Chinese, in the year 721, stated the quantity of this change at 1° in 83 years, which is at the rate of 43″ 1/2 per year. Other more modern astronomers have made this precession still more, but with some small differences from each other; and it is now usually taken at 50″ 1/4 per year. All these rates are deduced from a comparison of the longitude of certain stars as observed by more ancient astronomers, with the later observations of the same stars; viz. by subtracting the former from the latter, and dividing the remainder by the number of years in the interval between the dates of the observations. Thus, by a medium of a great number of comparisons, the quantity of the annual change has been fixed at 50″ 1/4, according to which rate it will require 25791 years for the equinoxes to make their revolution westward quite around the circle, and return to the same point again.|
Thus, by taking the longitudes of the principal stars established by Tycho Brahe, in his book Astronomiæ Instauratæ Progymnasmata, pa. 208 and 232, for the beginning of 1586, and comparing them with the same as determined for the year 1750, by M. de la Caille, for that interval of 164 years, there will be obtained the following differences of longitude of several stars; viz,
| g | Arietis | 2° | 17′ | 37″ |
| Aldebaran | 2 | 17 | 45 | |
| m | Geminorum | 2 | 17 | 1 |
| b | Geminorum | 2 | 15 | 26 |
| Regulus | 2 | 16 | 32 | |
| a | Virginis | 2 | 18 | 18 |
| a | Aquilæ | 2 | 19 | 1 |
| a | Pegasi | 2 | 16 | 12 |
| b | Libræ | 2 | 17 | 52 |
| Antares | 2 | 16 | 28 | |
| <*> | Tauri | 2 | 17 | 58 |
| g | Geminorum | 2 | 18 | 38 |
| g | Cancri | 2 | 19 | 12 |
| g | Leonis | 2 | 19 | 38 |
| g | Capricorni | 2 | 16 | 10 |
| Medium of these 15 stars | 2 | 17 | 35 |
The Ancients, and even some of the Moderns, have taken the equinoxes to be immoveable; and ascribed that change in the distance of the stars from it, to a real motion of the orb of the sixed stars, which they supposed had a slow revolution about the poles of the ecliptic; so as that all the stars perform their circuits in the ecliptic, or its parallels, in the space of 25,791 years; after which they should all return again to their former places.
This period the Ancients called the Platonic, or great year; and imagined that at its completion every thing would begin as at first, and all things come round in the same order as they have done before.
The phenomena of this retrograde motion of the equinoxes, or intersections of the equinoctial with the ecliptic, and consequently of the conical motion of the earth's axis, by which the pole of the equator describes a small circle in the same period of time, may be understood and illustrated by a scheme, as follows: Let NZSVL be the earth, SONA its axis produced to the starry heavens, and terminating in A, the present north pole of the heavens, which is vertical to N, the north pole of the earth. Let EOQ be the equator, T<*>Z the tropic of cancer, and VT<*> the tropic of capricorn; VOZ the ecliptic, and BO its axis, both of which are immoveable among the stars. But as the equinoctial points recede in the ecliptic, the earth's axis SON is in motion upon the earth's centre O, in such a manner as to describe the double cone NOn and SOs, round the axis of the ecliptic BO, in the time that the equinoctial points move round the ecliptic, which is 25,791 years; and in that length of time, the north pole of the earth's axis, produced, describes the circle ABCDA in the starry heavens, round the pole of the ecliptic, which keeps immoveable in the centre of that circle. The earth's axis being now 23° 28′ inclined to the axis of the ecliptic, the circle ABCDA, described by the north pole of the earth's axis produced to A, is 46° 56′ in diameter, or double the inclination of the earth's axis. In consequence of this, the point A, which is at present the north pole of the heavens, and near to a star of the 2d magnitude in the <*>nd of the Little Bear's tail, must be deserted by the earth's axis; which moving backwards 1 degree every 71 2/3 years nearly, will be directed towards the star or point B in 6447 3/4 years hence; and in double of that time, or 12,895 1/2 years, it will be directed towards the star or point C; which will then be the north pole of the heavens, although it is at present 8 1/2 degrees south of the zenith of London L. The present position of the equator EOQ will then be changed into eOq, the tropic of cancer T<*>Z into Vt<*>, and the tropic of capricorn VT<*> into t<*>Z; as is evident by the figure. And the sun, in the same part of the heavens where he is now over the earthly tropic of capricorn, and makes the shortest days and longest nights in the northern hemisphere, will then be over the earthly tropic of cancer, and make the days longest and nights shortest. So that it will require 12,895 1/2 years yet more, or from that time, to bring the north pole N quite round, so as to be directed toward that point of the heavens which is vertical to it at present. And then, and not till then, the same stars which at present describe the equator, tropics, and polar circles, &c, by the earth's diurnal motion, will describe them over again.
From this shifting of the equinoctial points, and with them all the signs of the ecliptic, it follows, that those stars which in the infancy of astronomy were in Aries, are now found in Taurus; those of Taurus in Gemini, &c. Hence likewise it is, that the stars which rose or set at any particular season of the year, in the times of Hesiod, Eudoxus, Virgil, Pliny, &c,| by no means answer at this time to their descriptions.
As to the physical cause of the Precession of the equinoxes, Sir Isaac Newton demonstrates, that it arises from the broad or slat spheroidal sigure of the earth; which itself arises from the earth's rotation about its axis: for as more matter has thus been accumulated all round the equatorial parts than any where else on the earth, the sun and moon, when on either side of the equator, by attracting this redundant manner, bring the equator sooner under them, in every return towards it, than if there was no such accumulation.
Sir Isaac Newton, in determining the quantity of the annual Precession from the theory of gravity, on supposition that the equatorial diameter of the earth is to the polar diameter, as 230 to 229, finds the sun's action sufficient to produce a Precession of 9″ 1/8 only; and collecting from the tides the proportion between the sun's force and the moon's to be as 1 to 4 1/2, he settles the mean Precession resulting from their joint actions, at 50″; which, it must be owned, is nearly the same as it has since been found by the best observations; and yet several other mathematicians have since objected to the truth of Sir Isaac Newton's computation.
Indeed, to determine the quantity of the Precession arising from the action of the sun, is a problem that has been much agitated among modern mathematicians; and although they seem to agree as to Newton's mistake in the solution of it, they have yet generally disagreed from one another. M. D'Alembert, in 1749, printed a treatise on this subject, and claims the honour of having been the first who rightly determined the method of resolving problems of this kind. The subject has been also considered by Euler, Frisius, Silvabelle, Walmesley, Simpson, Emerson, La Place, La Grange, Landen, Milner, and Vince.
M. Silvabelle, stating the ratio of the earth's axis to be that of 178 to 177, makes the annual Precession caused by the sun 13″ 52‴, and that of the moon - - 34 17; making the ratio of the lunar force to the solar, to be that of 5 to 2; also the nutation of the earth's axis caused by the moon, during the time of a semirevolution of the pole of the moon's orbit, i. e. in 9 1/3 years, he makes 17″ 51‴.—M. Walmesley, on the supposition that the ratio of the earth's diameters is that of 230 to 229, and the obliquity of the ecliptic to the equator 23° 28′ 30″, makes the annual Precession, owing to the sun's force, equal to 10″.583; but supposing the ratio of the diameters to be that of 178 to 177, that Precession will be 13″.675.—Mr. Simpson, by a different method of calculation, determines the whole annual precession of the equinoxes caused by the sun, at 21″ 6‴; and he has pointed out the errors of the computations proposed by M. Silvabelle and M. Walmesley.—Mr. Milner's deduction agrees with that of Mr. Simpson, as well as Mr. Vince's; and their papers contain besides several curious particulars relative to this subject. But for the various principles and reasonings of these mathematicians, see Philos. Trans. vol. 48, pa 385; vol. 49, pa. 704; vol. 69, pa. 505; and vol. 77. pa. 363; as also the writings of Simpson, Emer- son, Landen, &c; also De la Lande's Astronomie, and the Memoirs of the Acad. Sci. in several places.
As to the effect of the planets upon the equinoctial points, M. De la Place, in his new researches on this article, finds that their action causes those points to advance by 0″.2016 in a year, along the equator, or 0″.1849 along the ecliptic; from whence it follows that the quantity of the luni-solar Precession must be 50″.4349, since the total observed Precession is 50″ 1/4, or 50″.25.
To find the Precession in right ascension and declination. Put d = the declination of a star, and a = its right ascension; then their annual variations of Precessions will be nearly as follow: viz, 20″.084 X cos. a = the annual preces. in declinat. and 46″.0619 + 20″.084 X sin. a X tang. d = that of right ascension. See the Connoissance des Temps for 1792, pa. 206, &c.
