Preada Pereyra had recourse to the fabulous antiquities of the mite Precentor. Egyptians and Chaldeans, and to some idle rabbins, who imagined that there had been another world before that described by Moses. He was apprehended by the inquisition in Flanders, and very roughly used, though in the service of the dauphin. But he appealed from their sentence to Rome; whither he went in the time of Alexander VII. and where he printed a retraction of his book of Preadamites. See PRE-EXISTENCE. PREAMBLE, in Law, the beginning of an act of parliament, &c. which serves to open the intent of the act, and the mischiefs intended to be remedied by it. PREBEND, the maintenance a prebendary receives out of the estate of a cathedral or collegiate church. Prebends are distinguished into simple and dignitary: a simple prebend has no more than the revenue for its support; but a prebend with dignity has always a jurisdiction annexed to it. PREBENDARY, an ecclesiastic who enjoys a pre bend. The difference between a prebendary and a canon is, that the former receives his prebend in consideration of his officiating in the church, but the latter merely by his being received into the cathedral or college. PRECARIUM, in Scots Law. See Law, N° clxxxiii. 9. PRECEDENCE, a place of honour to which a person is entitled. This is either of courtesy or of right. The former is that which is due to age, estate, &c. which is regulated by custom and civility: the latter is settled by authority; and when broken in upon, gives an action at law. In Great Britain, the order of precedency is as follows: The king; the princes of the blood; the archbishop of Canterbury; the lord high chancellor; the archbishop of York; the lord treasurer of England; the lord president of the council; the lord privy seal; dukes; the eldest sons of dukes of the blood royal; marquises; dukes eldest sons; earls; marquises eldest sons; dukes younger sons; viscounts; earls eldest sons; marquises younger sons; bishops; barons; speaker of the house of commons; lord commissioner of the great seal; viscounts eldest sons; earls younger sons; barons eldest sons; privy counsellors not peers; chancellor of the exchequer; chancellor of the duchy; knights of the Garter not peers; lord chief justice of the king's bench; master of the rolls; lord chief justice of the common pleas; lord chief baron of the exchequer; puisne judges and barons; knights banneret, if made in the field; masters in chancery; viscounts younger sons; barons younger sons; baronets; knight banneret; knights of the Bath; knights bachelors; baronets eldest sons; knights eldest sons; baronets younger sons; knights younger sons; field and flag officers; doctors graduate; serjeants at law; esquires; gentlemen bearing coat armour; yeomen; tradesmen; artificers; labourers.—— Note, The ladies, except those of archbishops, bishops, and judges, take place according to the degree of quality of their husbands; and unmarried ladies take place according to that of their fathers. PRECEDENT, in Law, a case which has been determined, and which serves as a rule for all of the same nature. PRECENTOR, a dignity in cathedrals, popularly called the chanter, or master of the choir. PRECEPT, in Law, a command in writing sent by Precept a chief justice or justice of the peace, for bringing a person, record, or other matter before him. PRECEPT of Clarè Constat, in Scots Law. See LAW, Part III. N° clxxx. 28. PRECEPT of Seisin, in Scots Law. See Law, Part III. No clxiv. 16. PRECEPTIVE, any thing which gives or contains precepts. D Precession. I PRECEPTIVE Poetry. See POETRY, N° 146, &c. PRECESSION OF THE EQUINOXES. The most Diurnal reobvious of all the celestial motions is the diurnal revo-volution of lution of the starry heavens. The whole appears to heavens. the starry turn round an imaginary AXIS, which passes through two opposite points of the heavens, called the poles. One of these is in our sight, being very near the star a in the tail of the Little Bear. The great circle which is equidistant from both poles divides the heavens into the northern and southern hemispheres, which are equal. It is called the equator, and it cuts the horizon in the east and west points, and every star in it is 12 sidereal hours above and as many below the horizon, in each revolution. 2 Asiatic shepherds The sun's motions determine the length of day Observa and night, and the vicissitudes of the seasons. By a tions of the long series of observations, the shepherds of Asia were able to mark out the sun's path in the heavens; he being always in the opposite point to that which comes to the meridian at midnight, with equal but opposite declication. Thus they could tell the stars among which the sun then was, although they could not see them. They discovered that his path was a great circle of the heavens, afterwards called the ECLIPTIC; which cuts the equator in two opposite points, dividing it, and being divided by it, into two equal parts. They farther observed, that when the sun was in either of these points of intersection, his circle of diurnal revolution coincided with the equator, and therefore the days and nights were equal. Hence the equator came to be called the EQUINOCTIAL LINE, and the points in which it cuts the ecliptic were called the EQUINOCTIAL POINTS, and the sun was then said to be in the equinoxes. One of these was called the VERNAL and the other the AuTUMNAL EQUINOX. 3 time of the It was evidently an important problem in practical To deter astronomy to determine the exact moment of the sun's mine the occupying these stations; for it was natural to compute sun's occuthe course of the year from that moment. According- pying the ly this has been the leading problem in the astronomy equinoctial of all nations. It is susceptible of considerable preci- points. sion, without any apparatus of instruments. It is only necessary to observe the sun's declination on the noon of two or three days before and after the equinoctial day. On two consecutive days of this number, bis declination must have changed from north to south, or from south to north. If his declination on one day was observed to be 21' north, and on the next 5' south, it follows that his declination was nothing, or that he was in the equinoctial point about 23' after seven in the morning of the second day. Knowing the precise moments, and knowing the rate of the sun's motion in the ecliptic, it is easy to ascertain the precise point of the ecliptic in which the equator intersected it. chus's dis By a series of such observations made at Alexandria Hippar between the years 161 and 127 before Christ, Hippar- coveries. chus, 1 5. Precession, chus, the father of our astronomy, found that the point of the autumnal equinox was about six degrees to the eastward of the star called SPICA VIRGINIS. Eager to determine every thing by multiplied observations, he ransacked all the Chaldean, Egyptian, and other records, to which his travels could procure him access, for observations of the same kind; but he does not mention his having found any. He found, however, some observations of Aristillus and Timochares, made about 150 years before. From these it appeared evident that the point of the autumnal equinox was then about eight degrees east of the same star. He discusses these observations with great sagacity and rigour; and, on their authority, he asserts that the equinoctial points are not fixed in the heavens, but move to the westward about a degree in 75 years or somewhat less. 5 Why called This motion is called the PRECESSION OF THE EQUIthe preces- NOXES, because by it the time and place of the sun's sion of the equinoctial station precedes the usual calculations: it is equinoxes. fully confirmed by all subsequent observations. In 1750. the autumnal equinox was observed to be 20° 21′ westward of Spica Virginis. Supposing the motion to have been uniform during this period of ages, it follows that the annual precession is about 50"; that is, if the celestial equator cuts the ecliptic in a particular point on. any day of this year, it will on the same day of the fol lowing year cut it in a point 50" to the west of it, and the sun will come to the equinox 20' 23" before he has completed his round of the heavens. Thus the equinoctial or tropical year, or true year of seasons, is. so much shorter than the revolution of the sun or the sidereal year. 6 covery. Importance It is this discovery that has chiefly immortalized the of the dis- name of Hipparchus, though it must be acknowledged that all his astronomical researches have been conducted with the same sagacity and intelligence. It was natural therefore for him to value himself highly for this discovery; for it must be admitted to be one of the most singular that has been made, that the revolution of the whole heavens should not be stable, but its axis continually changing. For it must be observed, that since the equator changes its position, and the equator is only an imaginary circle, equidistant from the two poles or extremities of the axis; these poles and this axis must equally change their positions. The equinoctial points make a complete revolution in about 25,745 years, the equator being all the while inclined to the ecliptic in nearly the same angle. Therefore the poles of this diurnal revolution must describe a circle round the poles of the ecliptic at the distance of about 23 degrees in 25,745 years; and in the time of Timochares, the north pole of the heavens must have been 30 degrees eastward of the place where it now is. Hipparchus Hipparchus has been accused of plagiarism and inhas been sincerity in this matter. It is now very certain that accused of the precession of the equinoxes was known to the astroplagiarism. nomers of India many ages before the time of Hipparchus. It appears also that the Chaldeans had a pretty accurate knowledge of the year of seasons. From their saros we deduce their measure of this year to be 365 days 5 hours 49 minutes and 11 seconds, exceeding the truth only by 26", and much more exact than the year of Hipparchus. They had also a sidereal year of 365 days 6 hours II minutes. Now what could occasion an attention to two years, if they did not suppose the equinoxes moveable? The Egyptians also had a 7 knowledge of something equivalent to this; for they Precessiona had discovered that the dog-star was no longer the faithful forewarner of the overflowing of the Nile; and they * See Ducombined him with the star Fomelbaset in their mysti- pins sur le cal kalendar. This knowledge is also involved in the des Egypprecepts of the Chinese astronomy, of much older date tiens, Mem. than the time of Hipparchus. zodiaque de l'Acad. 8 But all these acknowledged facts are not sufficient des Inscrip. for depriving Hipparchus of the honour of the disce- But falsely. very, or fixing on him the charge of plagiarism. This motion was a thing unknown to the astronomers of the Alexandrian school, and it was pointed out to them by Hipparchus in the way in which he ascertained every other position in astronomy, namely, as the mathematical result of actual observations, and not as a thing deducible from any opinions on other subjects related to it. We see him on all other occasions, eager to confirm his own observations, and his deductions from them, by every thing he could pick up from other astronomers; and he even adduced the above-mentioned practice of the Egyptians in corroboration of his doctrine. It is more than probable then that he did not know any thing more. Had he known the Indian precession of 54" annually, he had no temptation whatever to withhold him from using it in preference to one which he acknowledges to be inaccurate, because deduced from the very short period of 150 years, and from the observations of Timochares, in which he had no great confidence.. 9 This motion of the starry heavens was long a matter Heavenly of discussion, as a thing for which no physical reason motions accould be assigned. But the establishment of the Co-counted for pernican system reduced it to a very simple affair; the pernican motion which was thought to affect all the heavenly system. bodies, is now acknowledged to be a deception, or a false judgment from the appearances. The earth turns round its own axis while it revolves round the sun, in the same manner as we may cause a child's top to spin on the brim of a millstone, while the stone is turning slowly round its axis. If the top spin steadily, without any wavering, its axis will always point to the zenith of the heavens; but we frequently see, that while it spins briskly round its axis, the axis itself has a slow conical motion round the vertical line, so that, if produced, it would slowly describe a circle in the heavens round the zenith point. The flat surface of the top may represent the terrestrial equator, gradually turning itself round on all sides. If this top were formed like a ball, with an equatorial circle on it, it would represent the whole motion very prettily, the only difference being, that the spinning motion and this wavering motion are in the same direction; whereas the diurnal rotation and the motion of the equinoctial points are in contrary directions. Even this dissimilarity may be removed, by making the top turn on a cap, like the card of a mariner's compass. ΤΟ It is now a matter fully established, that while the And the earth revolves round the sun from west to east, in the earth's. plane of the ecliptic in the course of a year, it turns round its own axis from west to east in 23h 56′ 4′′, which axis is inclined to this plane in an angle of nearly 23° 28′; and that this axis turns round a line perpendicular to the ecliptic in 25,745 years from east to west, keeping nearly the same inclination to the ecliptic.By this means, its pole in the sphere of the starry heavens describes a circle round the pole of the ecliptic at the 14 of the equa Precession. the distance of 23° 28' nearly. The consequence of Let E (fig. 1.), be the pole of the ecliptic, and SPQ Precession. this must be, that the terrestrial equator, when produ- a circle distant from it 23° 28', representing the circle ced to the sphere of the starry heavens, will cut the described by the pole of the equator during one revolu- Plate ecliptic in two opposite points, through which the sun tion of the equinoctial points. Let P be the place of ccccxxxvi must pass when he makes the day and night equal; and this last mentioned pole at some given time. Round P fig. 1. that these points must shift to the westward, at the rate describe a circle ABCD, whose diameter AC is 18". Mathemaof 50 seconds annually, which is the precession of the The real situation of the pole will be in the circum-tical theory equinoxes. Accordingly this has been the received ference of this circle; and its place, in this circum- if the poles doctrine among astronomers for nearly three centuries, ference, depends on the place of the moon's ascending or be supe and it was thought perfectly conformable to appearnode. Draw EPF and GPL perpendicular to it; let posed to deGL be the colure of the equinoxes, and EF the colure scribe a cirof the solstices. Dr Bradley's observations showed that cle. the pole was in A when the node was in L, the vernal equinox. If the node recede to H, the winter solstice, the pole is in B. When the node is in the autumnal equinox at G, the pole is at C; and when the node is in F, the summer solstice, the pole is in D. In all intermediate situations of the moon's ascending node, the pole is in a point of the circumference ABCD, three signs or 90° more advanced. Bradley's discover bit. ances. But Dr Bradley, the most sagacious of modern astroattempts to nomers, hoped to discover the parallax of the earth's orbit by observations of the actual position of the pole of the parallax of the the celestial revolution. Dr Hooke had attempted this earth's or- before, but with very imperfect instruments. The art of observing being now prodigiously improved, Dr Bradley resumed this investigation. It will easily appear, that if the earth's axis keeps parallel to itself, its extremity must describe in the sphere of the starry heavens a figure equal and parallel to its orbit round the sun; and if the stars be so near that this figure is a visible object, the pole of diurnal revolution will be in different distinguishable points of this figure. Consequently, if the axis describes the cone already mentioned, the pole will not describe a circle round the pole of the ecliptic, but will have a looped motion along this circumference, similar to the absolute motion of one of Jupiter's satellites, describing an epicycle whose centre describes the circle round the pole of the ecliptic. 12 Difficulties in the attempt obviated by accident. 13 His further He accordingly observed such an epicyclical motion, and thought that he had now overcome the only difficulty in the Copernican system; but, on maturely considering his observations, he found this epicycle to be quite inconsistent with the consequences of the annual parallax, and it puzzled him exceedingly. One day, while taking the amusement of sailing about on the Thames, he observed, that every time the boat tacked, the direction of the wind, estimated by the direction of the vane, seemed to change. This immediately suggested to him the cause of his observed epicycle, and he found it an optical illusion, occasioned by a combination of the motion of light with the motion of his telescope while observing the polar stars. Thus be unwittingly established an incontrovertible argument for the truth of the Copernican system, and immortalized his name by his discovery of the ABERRATION of the stars. He now engaged in a series of observations for asinvestiga certaining all the circumstances of this discovery. In tion of the the course of these, which were continued for 28 years, subject. he discovered another epicyclical motion of the pole of the heavens, which was equally curious and unexpected. He found that the pole described an epicycle, whose diameter was about 18", having for its centre that point of the circle round the pole of the ecliptic in which the pole would have been found independent of this new motion. He also observed, that the period of this epicyclical motion was 18 years and seven months. It struck him, that this was precisely the period of the revolution of the nodes of the moon's orbit. He gave a brief account of these results to Lord Macclesfield, then president of the Royal Society, in 1747. Mr Machin, to whom he also communicated the observations, gave him in return a very neat mathematical hypothesis, by fig. 1. which the motion might be calculated. Plate ccccxxxviii 3 eircle. Dr Bradley, by comparing together a great number More exact of observations, found that the mathematical theory, and it an ele the calculation depending on it, would correspond much bett better with the observations, if an ellipse were substituted for the ed for the circle ABCD, making the longer axis AC 18", and the shorter, BD, 16". Mr d'Alembert determined, by the physical theory of gravitation, the axes to be 18" and 13".4. 16 and this These observations, and this mathematical theory, These ob must be considered as so many facts in astronomy, and servations we must deduce from them the methods of computing theory are the places of all celestial phenomena, agreeable to the facts in universal practice of determining every point of the hea- astronomy. vens by its longitude, latitude, right ascension, and declination. 17 It is evident, in the first place, that this equation of Obliquity the pole's motion makes a change in the obliquity of of the the ecliptic. The inclination of the equator to the eclip-ecliptic. tic is measured by the arch of a great circle intercepted between their poles. Now, if the pole be in O instead of P, it is plain that the obliquity is measured by EO instead of EP. If EP be considered as the mean obliquity of the ecliptic, it is augmented by 9" when the moon's ascending node is in the vernal equinox, and consequently the pole in A. It is, on the contrary, diminished 9" when the node is in the autumnal equinox, and the pole in C; and it is equal to the mean when the node is in the colure of the solstices. This change of the inclination of the earth's axis to the plane of the ecliptic was called the NUTATION of the axis by Sir Isaac Newton; who shewed, that a change of nearly a second must obtain in a year by the action of the sun on the prominent parts of the terrestrial spheroid. But he did not attend to the change which would be made in this motion by the variation which obtains in the disturbing force of the MOON, in consequence of the different obliquity of her action on the equator, arising from the motion of her own oblique orbit. It is this change which now goes by the name NUTATION, and we owe its discovery entirely to Dr Bradley. The general change of the position of the earth's axis has been termed DEVIATION by modern astronomers. 19 Change of the equinoctial points. Precession, and that PM is its cosine; and (on account of the small- theirs. When the pole is at P, the right ascension of Precession. ness of AP in comparison of EP) PM may be taken for S from the solstitial colure is measured by the angle the change of the obliquity of the ecliptic. This is there- SPE, contained between that colure and the star's circle fore 9" X cos. long. node, and is additive to the of declination. But when the pole is at O, the right mean obliquity, while O is in the semicircle BAD, that ascension is measured by the angle SOE, and the dif is, while the longitude of the node is from 9 signs to 3 ference of SPE and SOE is the equation of right assigns; but subtractive while the longitude of the node cension. The angle SOE consists of two parts, GOE changes from 3 to 9 signs. and GOS; GOE remains the same wherever the star S is placed, but GOS varies with the place of the star.We must first find the variation by which GPE becomes GOE, which variation is common to all the stars. The triangles GPE, GOE, have a constant side GE, and a constant angle G; the variation PO of the side GP is extremely small, and therefore the variation of the angles may be computed by Mr Cotes's Fluxionary Theorems. See Simpson's Fluxions, § 253, &c. As the tangent of the side EP, opposite to the constant angle G, is to the sine of the angle EPG, opposite to the constant side EG, so is PO the variation of the side GP, adjacent to the constant angle, to the variation of the angle GPO, opposite to the constant side EG. This gives 9" sin. long. node This is subtractive from the 20 Situation of the sol stitial and equinoctial colures. 21 nutation of axis. But the nutation changes also the longitudes and right ascensions of the stars and planets, by changing the equinoctial points, and thus occasioning an equation in the precession of the equinoctial points. It was this circumstance which made it necessary for us to consider it in this place, while expressly treating of this precession. Let us attend to this derangement of the equinoctial points. The great circle or meridian which passes through Equation 22 This equation of longitude is the same for all the stars, for the longitude is reckoned on the ecliptic (which is here supposed invariable); and therefore is affected only by the variation of the point from which the longitude is computed. The right ascension, being computed on the equator, Right ascension suf suffers a double change. It is computed from, or befers a dou- gins at, a different point of the equator, and it termible change. nates at a different point; because the equator having changed its position, the circles of declination also change VOL. XVII. Part I. tang. obl. eclip. mean right ascension for the first six signs of the node's &c. 23 The variation of the other part SOG of the angle, Other va which depends on the different position of the hour riations, circles PS and OS, which causes them to cut the equation in different points, where the arches of right ascension terminate, may be discovered as follows: The triangles SPG, SOG, have a constant side SG, and a constant angle G. Therefore, by the same Cotesian theorem, tan. SP: sin. SPG = PO: y, and y, or the second part of the nutation in right ascension, = 9′′ × sin. diff. R. A of star and node exact mode nomical researches, founded on Machin's Theory. When of calcula- 26 It now remains to consider the precession of the equiPrecession, noctial points, with its equations, arising from the nutaof the equinoctial tion of the earth's axis as a physical phenomenon, and points, &c. to endeavour to account for it upon those mechanical principles which have so happily explained all the other phenomena of the celestial motions. 27 Precession. sion, for some hundreds of the principal stars, for every tates to the sun in the direction MS, which is all above Precess it. position of the moon's node and of the sun. the ecliptic, it is plain that this gravitation has a tendency to draw the moon towards the ecliptic. Suppose this force to be such that it would draw the moon down from M to i in the time that she would have moved from M to t, in the tangent to her orbit. By the combination of these motions, the moon will desert her orbit, and describe the line Mr, which makes the diagonal of the parallelogram; and if no farther action of the sun be supposed, she will describe another orbit Mdn', lying between the orbit MCD n and the ecliptic, and she will come to the ecliptic, and pass through it in a point n', nearer to M than n is, which was the former place of her descending node. By this change of orbit, the line EX will no longer be perpendicular to it; but there will be another line Ex, which will now be perpendicular to the new orbit. Also the moon, moving from M to r, does not move as if she had come from the ascending node N, but from a point N lying beyond it; and the line of the nodes of the orbit in this new position is N''. Also the angle MN'm is less than the angle MNm. Observations of Newton and others on this subject. 28 Sketch of This did not escape the penetrating eye of Sir Isaac Let S (fig. 2.) be the sun, E the earth, and M the investiga moon, moving in the orbit NMCD n, which cuts the ion of it. plane of the ecliptic in the line of the nodes Nn, and Fig. 2. has one half raised above it, as represented in the figure, the other half being hid below the ecliptic. Suppose this orbit folded down; it will coincide with the ecliptic in the circle Nm c dn. Let EX represent the axis of this orbit, perpendicular to its plane, and therefore inclined to the ecliptic. Since the moon gravi Thus the nodes shift their places in a direction opposite to that of her motion, or move to the westward; the axis of the orbit changes its position, and the orbit. itself changes its inclination to the ecliptic. These momentary changes are different in different parts of the orbit, according to the position of the line of the nodes. Sometimes the inclination of the orbit is increased, and sometimes the nodes move to the eastward. But, in general, the inclination increases from the time that the nodes are in the line of syzigee, till they get into quadrature, after which it diminishes till the nodes are again in syzigee. The nodes advance only while they are in the octants after the quadratures, and while the moon passes from quadrature to the node, and they recede in all other situations. Therefore the recess exceeds the advance in every revolution of the moon round the earth, and, on the whole, they recede. What has been said of one moon, would be true of each of a continued ring of moons surrounding the earth, and they would thus compose a flexible ring, which would never be flat but waved, according to the difference (both in kind and degree) of the disturbing forces acting on its different parts. But suppose these moons to colère, and to form a rigid and flat ring, nothing would remain in this ring but the excess of the contrary tendencies of its different parts. Its axis would be perpendicular to its plane, and its position in any moment will be the mean position of all the axes of the orbits of each part of the flexible ring; therefore the nodes of this rigid ring will continually recede, except when the plane of the ring passes through the sun, that is, when the nodes are in syzigee; and (says Newton) the motion of these nodes will be the same with the mean motion of the nodes of the orbit of one moon. The incli nation of this ring to the ecliptic will be equal to the mean inclination of the moon's orbit during any one revolution which has the same situation of the nodes. It will therefore be least of all when the nodes are in quadrature, and will increase till they are in syzigee, and then diminish till they are again in quadrature. Suppose this ring to contract in dimensions, the disturbing forces will diminish in the same proportion, and in this proportion will all their effects diminish. Sup pose |