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Preada. Pereyra lad recourse to the fabulous antiquities of the PRECEPT, in Law, a command in writing sent by Precepe mite Egyptians and Chaldeans, and to some idle rabbins, who a chief justice or justice of the peace, for bringing a

imagined that there had been another world before that person, record, or other matter before bim.

described by Moses. He was apprehended by the in PRECEPT of Clarè Constat, in Scots Law. See Lai,
quisition in Flanders, and very roughly used, though in Part III. No clxxx. 28.
the service of the dauphin. But be appealed from their PRECEPT of Seisin, in Scots Law. See Law, Part
sentence to Rome ; whither he went in the time of III. No clxiv. 16.
Alexander VII. and where he printed a retraction of PRECEPTIVE, any thing which gives or contains
his book of Preadamites. See PRE-EXISTENCE. precepts.

PREAMBLE, in Law, the beginning of an act of PRECEPTIE Poetry. See POETRY, No 146, &c. parliament, &c. which serves to open the intent of the PRECESSION OF THE EQUINOXES. The most Diurnal a act, and the mischiefs intended to be remedied by it. obvious of all the celestial motions is the diurnal

voltage PREBEND, the maintenance a prebendary receives lution of the starry heavens. The whole appears to

beatthi. out of the estate of a cathedral or collegiate church. turn round an imaginary axis, which passes througla Prebends are distinguished into simple and dignitary: a two opposite points of the heavens, called the poles. One simple prebend bas no more than the revenue for its of these is in our sight, being very near the star a in support; but a prebend with dignity has always a juris- the tail of the Little Bear. The great circle which is diction annexed to it.

equidistant from both poles divides the heavens into the PREBENDARY, an ecclesiastic who enjoys a pre northern and southern hemispheres, which are equal. bend.

It is called the equator, and it cuts the horizon in the The difference between a prebendary and a canon is, east and west points, and every star in it is 12 sidereal that the former receives his prebend in consideration of hours above and as many below the horizon, in each his officiating in the church, but the latter merely by revolution. bis being received into the cathedral or college.

The sun's motions determine the length of day Obsery PRECARIUM, in Scots Law. See Law, No and night, and the vicissitudes of the seasons. By a tions et de clxxxiii. 9.

long series of observations, the shepherds of Asia were PRECEDENCE, a place of honour to which a ,

able to mark out the sun's path in the heavens; he person is entitled. This is either of courtesy or of right. being always in the opposite point to that which comes The former is that which is due to age, estate, &c. to the meridian at midnight, with equal but opposite which is regulated by custom and civility: the latter is declication. Thus they could tell the stars among settled by authority; and when broken in upon, gives which the sun then was, although they could not see an action at law.

them. They discovered that his path was a great circle In Great Britain, the order of precedency is as fol of the heavens, afterwards called the ECLIPTIC ; which lows: The king; the princes of the blood; the arch cuts the equator in two opposite points, dividing it, and bishop of Canterbury; the lord high chancellor ; the being divided by it, into two equal parts. They fararchbishop of York; the lord treasurer of England ; ther observed, that when the sun was in either of these the lord president of the council ; the lord privy seal; points of intersection, bis circle of diurnal revolution dukes; the eldest sons of dukes of the blood royal ; mar coincided with the equator, and therefore the days and quises; dukes eldest sons; earls ; marquises eldest nights were equal. Hence the equator came to be calsons ; dukes younger sons ; viscounts; earls eldest sons ; led the EQUINOCTIAL LINE, and the points in which it marquises younger sons; bishops; barons ; speaker of cuts the ecliptic were called the EQUINOCTIAL POINTS, the house of commons ; lord commissioner of the great and the sun was then said to be in the equinoxes. One seal; viscounts eldest sons ; earls younger sons; barons of these was called the VERNAL and the other the Aueldest sons ; privy counsellors not peers ; chancellor of TUMNAL Equinox. the exchequer; chancellor of the duchy; kuights of the It was evidently an important problem in practical To deterGarter not peers;

lord chief justice of the king's bench; astronomy to determine the exact moment of the sun's master of the rolls; lord chief justice of the common occupying these stations; for it was natural to compute pleas; lord chief baron of the exchequer; puisne judges the course of the year from that moment. According- pying us and barons ; knights banneret, if made in the field; ly this has been the leading problem in the astronomy equiries masters in chancery; viscounts younger sons; barons of all nations. It is susceptible of considerable preci- points. younger sons; baronets; knight banneret ; knights of sion, without any apparatus of instruments. It is only the Bath ; kuights bachelors ; baronets eldest sons ; necessary to observe the sun's declination on the noon knights eldest sons; baronets younger sons; knights of two or three days before and after the equinoctial younger sons ; field and flag officers ; doctors graduate; day. On two consecutive days of this number, bis de. serjeants at law; esquires; gentlemen bearing coat ar clination must have chauged from north to south, or mour; yeomen; tradesmen ; artificers ; labourers.. from south to north. If his declination on one day was Note, The ladies, except those of archbishops, bishops, observed to be 21' north, and on the next s' souih, it and judges, take place according to the degree of qua- follows that his declination was nothing, or that he was lity of their husbands; and unmarried ladies take place in the equinoctial point about 23' after seven in the according to that of their fathers.

morning of the second day. Knowing the precise moPRECEDENT, in Law, a case which has been de- ments, and knowing the rate of the sun's motion in the termined, and wbich serves as a rule for all of the same ecliptic, it is easy to ascertain the precise point of the nature.

ecliptic in wbich the equator intersected it. PRECENTOR, a dignity in cathedrals, popularly By a series of such observations made at Alexandria Hippar called the chanter, or master of the chuir.

between the years 161 and 127 before Christ, Hippar.


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sidereal year.

Precession. chus, the father of our astronomy, found that the point knowledge of something equivalent to this; for they Precession.

of the autumnal equinox was about six degrees to the had discovered that the dog-star was no longer the faith-
eastward of the star called SPICA VIRGINIS. Eager to ful forewarner of the overflowing of the Nile; and they * See Do-
determine every thing by multiplied observations, he combined him with the star Fomelbaset * in their mysti- pins sur le
ransacked all the Chaldean, Egyptian, and other records, cal kalendar. This knowledge is also involved in the des Egyp-
to which his travels could procure him access, for obser precepts of the Chinese astronomy, of much older date tiens, Mem.
vations of the same kind; but he does not mention his than the time of Hipparchus.

de l'Acad. having found any. He found, however, some observa But all these acknowledged facts are not suflicient des Inscrip. tions of Aristillus and Timochares, made about 150 years for depriving Hipparchus of the honour of the disco- Bat falsely

. before. From these it appeared evident that the point very, or fixing on him the charge of plagiarism. This of the autumnal equinox was then about eight degrees motion was a thing unknown to the astronomers of the east of the same star. He discusses these observations Alexandrian school, and it was pointed out to them with great sagacity and rigour ; and, on their authority, by Hipparchus in the way in which he ascertained he asserts that the equinoctial points are not fixed in every other position in astronomy, namely, as the ma

the heavens, but move to the westward about a degree thematical result of actual observations, and not as a 5 in 75 years or somewhat less.

thing deducible from any opinions on other subjects re* Why called This motion is called the PRECESSION OF THE Equi. lated to it. We see him on all other occasions, eager to = the preces. Noxes, because by it the time and place of the sun's confirm his own observations, and his deductions from sion of the

equinoctial station precedes the usual calculations : it is them, by every thing he could pick up from other astro, equinoxes.

fully confirmed by all subsequent observations. In 17.50. nomers; and he even adduced the above-mentioned
the autumnal equinox was observed to be 20° 21' west practice of the Egyptians in corroboration of his doc-
ward of Spica Virginis. Supposing the motion to have trine. It is more than probable then that he did not
been uniform during this period of ages, it follows that know any thing more. Had he known the Indian
the annual precession is about 50"}; that is, if the cem precession of 54" annually, he had no temptation what-
lestial equator cuts the ecliptic in a particular point on. ever to withhold him from using it in preference to one
any day of this year, it will on the same day of the fol. which he acknowledges to be inaccurate, because de-
lowing year cut it in a point 50"} to the west of it, duced from the very short period of 150 years, and from
and the sun will come to the equinox 20' 23" before he the observations of Timochares, in which he had no
has completed his round of the heavens. Thus the great confidence.
equinoctial or tropical year, or true year

of seasons, is. This motion of the starry heavens was long a matter Heavenly so much shorter than the revolution of the sun or the of discussion, as a thing for which no physical reason motions ac

could be assigned.
But the establishmrnt of the Co-counted for:

by the Co. Importance It is this discovery that has chiefly immortalized the pernican system reiluced it to a very simple affair ; tbe

pernican of the dis- name of Hipparchus, though it must be acknowledged

motion which was thought to affect all the heavenly system. covery.

that all bis astronomical researches have been conducted bodies, is now acknowledged to be a deception, or a
with the same sagacity and intelligence. It was natural false judgment from the appearances. The earth turns
therefore for him to value himself highly for this disco round its own axis while it revolves round the sun, in
very; for it must be admitted to be one of the most the same manner as we may cause a child's top to spin
singular that has been made, that the revolution of the on the brim of a millstone, while the stone is turning
whole heavens should not be stable, but its axis conti slowly round its axis. If the top spin steadily, with-
nually changing. For it must be observed, that since out any wavering, its axis will always point to the ze-
the equator changes its position, and the equator is only nith of the heavens; but we frequently see, that while
an imaginary circle, equidistant from the two poles or it spins briskly round its axis, the axis itself has a slow.
extremities of the axis ; these poles and this axis. must conical motion round the vertical line, so that, if pro-
equally change their positions. The equinoctial points duced, it would slowly describe a circle in the heavens
make a complete revolution in about 25,745 years, the round the zenith point. The flat surface of the top may
equator being all the while inclined to the ecliptic in represent the terrestrial equator, gradually turning itself
nearly the same angle. Therefore the poles of this diurnal round on all sides. If this lop were formed like a ball,
revolution must describe a circle round the poles of the with an equatorial circle on it, it would represent the
ecliptic at the distance of about 23 degrees in 25,745 whole motion very prettily, the only difference being,
years; and in the time of Timochares, the north pole that the spinning motion and this wavering motion are
of the heavens must have been 30 degrees eastward of in the same direction; whereas the diurnal rotation and

tbe place where it now is. 7.

the motion of the equinoctial points are in contrary di-
Hipparchus. Hipparchus has been accused of plagiarism and ina rections. Even this dissimilarity may be removed, by
has been sincerity in this matter. It is now very certain that making the top turn on a cap, like the card of a mari-
accused of the precession of the equinoxes was known to the astro ner's compass.

nomers of India many ages before the time of Hippar It is now a matter fully established, that while the And the
chus. It appears also that the Chaldeans had a pret earth revolves round the sun from west to east, in the earth's.;
ty accurate knowledge of the year of seasons. From plane of the ecliptic in the course of a year, it turns
their saros we deduce their measure of this year to be round its own axis from west to east in 23h 56' 4",
365 days 5 hours 49 minutes and 11 seconds, exceeding which axis is inclined to this plane in an angle of nearly
the truth only by 26", and much more exact than the 23° 28'; and that this axis turns round a line perpen-
year of Hipparchus

. They had also a sidereal year of dicular to the ecliptic in 25,745 years from east to west,
365 days 6 hours 11 minutes. Now what could occa keeping nearly the same inclination to the ecliptic.-
sion an attention to two years, if they did not suppose By this means, its pole in the sphere of the starry hea-
the equinoxes moveable? The Egyptians also had a vens describes a circle round the pole of the ecliptic at


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said, that when the pole is in 0, the arch ADCO is ascertain

Precession. the distance of 23° 28' nearly. The consequence of Let E (ay. 1.), be the pole of the ecliptic, and SPQPrecession,

this must be, that the terrestrial equator, when produ a circle distant from it 23° 28', representing the circler 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 Ceccat vi 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 bas 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 rot be sua and it was thought perfectly conformable to appear node. Draw EPF and GPL perpendicular to it; let posed to deances.

GL be the colure of the equinoxes, and EF the colore scribe a cirBradley's Bat Dr Bradley, the most sagacious of modern astro of the solstices. Dr Bradley's observations showed that eles attempts to

nomers, hoped to discover the parallax of the earth’s or the pole was in A when the node was in L, the vernal discover

bit by observations of the actual position of the pole of equinox. If the node recede to H, the winter solstice, the parallax the celestial revolution. Dr Hooke had attempted this the pole is in B. When the node is in the autumnal earth's or- before, but with very imperfect instruments. The art equinox at G, the pole is at C; and when the node is bit.

of observing being now prodigiously improved, Dr Brad in F, the summer solstice, the pole is in D. In all in-
ley resumed this investigation. It will easily appear, termediate situations of the moon's ascending node, the
that if the earth’s axis keeps parallel to itself, its extre pole is in a point of the circumference ABCD, three
mity must describe in the sphere of the starry heavens signs or 90° more advanced.
a figure equal and parallel to its orbit round the sun; Dr Bradley, hy comparing together a great number More exact
and if the stars be so near that this figure is a visible ob of observations, found that the mathematical theory, and is an elipse
ject, the pole of diurnal revolution will be in different the calculation depending on it, would correspond much be substitz-
distinguishable points of this figure. Consequently, if better with the observations, if an ellipse were substitut-
tbe axis describes the cone already mentioned, the pole ed for the circle ABCD, making the longer axis AC
will not describe a circle round the pole of the ecliptic, 18", and the shorter, BD, 16". Mr d'Alembert deter-
but will have a looped motion along this circumference, mined, by the physical theory of gravitation, the axes to
similar to the absolute motion of one of Jupiter's satel be 18" and 13".4.
lites, describing an epicycle whose centre describes the These observations, and this mathematical theory, These ob-
circle round the pole of the ecliptic.

must be considered as so many facts in astronomy, and servations Difficulties

He accordingly observed such an epicyclical motion, we must deduce from them the methods of computing and this In the at

the places of all celestial phenomena, agreeable to the facts in and thought that he had now overcome the only diffitempt obviated by culty in the Copernican system ; but, on maturely con universal practice of determining every point of the hea astronomy. accident. sidering his observations, he found this epicycle to be vens by its longitude, latitude, right ascension, and dequite inconsistent with the consequences of the annual clination.

17 parallax, and it puzzled him exceedingly. One day, It is evident, in the first place, that this equation of obliquity while taking the amusement of sailing about on the the pole's motion makes a change in the obliquity of of the Thames, he observed, that every time the boat tacked, the ecliptic. The inclination of the equator to the eclip-ecliptie

. the direction of the wind, estimated by the direction of tic is measured by the arch of a great circle intercepthe vane, seemed to change. This immediately sug ted between their poles. Now, if the pole be in 0 ingested to him the cause of his observed epicycle, and stead of P, it is plain that the obliquity is measured by he found it an optical illusion, occasioned by a combi EO instead of EP. If EP be considered as the mean nation of the motion of light with the motion of his obliquity of the ecliptic, it is augmented by g" when telescope while observing the polar stars. Thus be on the moon's ascending node is in the vernal equinox, and wittingly established an incontrovertible argument for consequently the pole in A. It is, on the contrary, dithe truth of the Copernican system, and immortalized minished 9" when the node is in the autumnal equinox, his name by his discovery of the ABERRATION of the and the pole in C; and it is equal to the mean when

the node is in the colure of the solstices. This change 13 His further He now engaged in a series of observations for as of the inclination of the earth's axis to the plane of the investiga- certaining all the circumstances of this discovery. In ecliptic was called the NUTATION of the axis by Sir Isaac tion of the the course of these, which were continued for 28 years, Newton ; who shewed, that a change of nearly a second subject

he discovered another epicyclical motion of the pole of must obtain in a year by the action of the sun on the the heavens, which was equally curious and unexpected. prominent parts of the terrestrial spheroid. But he did He found that the pole described an epicycle, whose not attend to the change which would be made in this diameter was about 18", having for its centre that point motion by the variation which obtains in the disturbing of the circle round the pole of the ecliptic in which the force of the Moon, in consequence of the different oblipole would have been found independent of this new quity of her action on the equator, arising from the mo. motion. He also observed, that the period of this epi tion of her own oblique orbit. It is this change which cyclical motion was 18 years and seven months. It now goes by the name NUTATION, and we owe its disstruck him, that this was precisely the period of the re covery entirely to Dr Bradley. The general change volution of the nodes of the moon's orbit. He gave a of the position of the earth's axis has been termed DEbrief account of these results to Lord Macclesfield, then VIATION by modern astronomers.

president of the Royal Society, in 1747. Mr Machin, The quantity of this change of obliquity is easily as- Quantity or Plate

to whom he also communicated the observations, gave certained. It is evident, from what has been already it easily ccccxxxviii him in return a very neat mathematical bypothesis, by fig. 1. which the motion might be calculated.

equal to the node's longitude from the vernal equinox,






Precessiou, 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 0, 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 as-

signs; but subtractive while the longitude of the node cension. The angle SOE consists of two parts, GOE 19 changes from 3 to 9 signs.

and GOS; GOE remains the same wherever the star S Change of

But the nutation changes also the longitudes and right is placed, but GOS varies with the place of the star.the equi

ascensions of the stars and planets, by changing the equi- We must first find the variation by which GPE becomes points.

noctial points, and thus occasioning an equation in the GOE, wbich variation is common to all the stars. The
precession of the equinoctial points. It was this circum- triangles GPE, GOE, have a constant side GE, and a
stance which made it necessary for us to consider it in constant angle G; the variation PO of the side GP is
this place, while expressly treating of this precession. extremely small, and therefore the variation of the angles
Let us attend to this derangement of the equinoctial may be computed by Mr Cotes's Fluxionary Theorems.

See Simpson's Fluxions, § 253, &c. As the tangent of
Situation The great circle or meridian which passes through the side EP, opposite to the constant angle G, is to the
of the sol the poles of the ecliptic and equator is always the solsti sine of the angle EPG, opposite to the constant side
stitial and tial colure, and the equinoctial colure is at right angles EG, so is PO"the variation of the side GP, adjacent to

to it: therefore when the pole is in P or in 0, FP or the constant angle, to the variation x of the angle
EO is the solstitial colure. Let S be any fixed star or GPO, opposite to the constant side EG. This gives
planet, and let SE be a meridian or circle of longitude ; 9" X sin. long. node
draw the circles of declination PS, OS, and the circles

This is subtractive from the

tang. obl. eclip. M'EM", mEm', perpendicular to PE, OE.

mean right ascension for the first six signs of the node's Equation

If the pole were in its mean place P, the equinoctial longitude, and additive for the last six signs. This equaot tongi points would be in the ecliptic meridian M EM", or that tion is common to all the stars. tude from meridian would pass through the intersections of the The variation of the other part SOG of the angle, Other vathe earth's equator and ecliptic, and the angle M’ES would mea

wbich de pends on the different position of the hour riations, axis. . sure the longitude of the star S.

&c. But when the pole is circles PS and OS, which causes them to cut the equain 0, the ecliptic meridian mEm' will pass through tion in different points, where the arches of right ascenthe equinoctial points. The equinoctial points must sion terminate, may be discovered as follows : The tritherefore be to the westward of their mean place, and angles SPG, SOG, have a constant side SG, and a the equation of the precession must be additive to that constant angle G. Therefore, by the same Cotesian precession : and the longitude of the star S will now be theorem, tan. SP : sin. SPG PO : measured by the angle m Es, which, in the case here second part of the nutation in right ascension, = represented, is greater than its mean longitude. The g" X sin. diff. R. A of star and node difference or the equation of longitude, arising from the

cotan. declin. star OM

24 nutation of the earth's axis, is the angle OEP, or

The nutation also affects the declination of the stars : Nutation

OE* For SP, the mean codeclination, is changed into so.- affecte the OM is the sine of the angle CPO, which, by what has suppose a circle described round S, with the distance

uion of the been already observed, is equal to the longitude of the SO cutting SP in f; then it is evident that the equamode : Therefore OM is equal to 9" x long. node, and tion of declin. is Pf= PO X cosine OPf = 9" x sign OM.

9" x sin. long. node is equal to

This equation is

r. ascen. of star-long.of node.
sis. oblig.eclip.

Such are the calculations in constant use in our astro-A more
additive to the mean longitude of the star when O is in nomical researches, founded on Machin’s Theory. When exact mode
the semicircle CBA, or while the ascending node is pas- still greater accuracy is required, the elliptical theory con.
sing backwards from the vernal to the autumnal equi- must be substituted, by taking (as is expressed by the
nox; but it is subtractive from it while O is in the semi- dotted lines) O in that point of the ellipse described on
circle ADC, or while the node is passing backwards the transverse axis AC, where it is cut by OM, drawn
from the autumnal to the vernal equivox ; or, to express according to Machin's Theory. All the change made
it more briefly, the equation is subtractive froin the mean here is the diminution of OM in the ratio of 18 to 13.4,
longitude of the star, while the ascending node is in the and a corresponding diminution of the angle CPO. The
first six signs, and additive to it while the node is in the detail of it may be seen in De la Lande's Astronomy,
last six signs.

art. 2874; but is rather foreign to our present purpose This equation of longitude is the same for all the stars of explaining the precession of the equinoxes. The calfor the longitude is reckoned on the ecliptic (which is culations being in every case tedious, and liable to misliere supposed invariable); and therefore is affected only takes, on account of the changes of the signs of the difby the variation of the point from which the longitude ferent equations, thi zealous pronoters of astronomy have is computed.

calculated and published tables of all these equations, Right as

The right ascension, being computed on the equator, both on the circular and elliptical hypothesis. And still ension suf suffers a double change. It is computed from, or be more to abridge calculations, which occur in reducing ers a dou gins at, a different point of the equator, and it termi- every astronomical observation, when the place of a phe» le change. nates at a different point; because the equator having nomenon is deduced from a comparison with known stars,

changed its position, the circles of declination also change there have been published tables of nutation and preces-
Vol. XVII. Part I.




y, and

y, or the





Precession. sion, for some hundreds of the principal stars, for every tutes to the sun in the direction MS, which is all abore preceae's position of the moon's node and of the sun.

the ecliptic, it is plain that this gravitation las a tenIt now remains to consider the precession of the equi dency to draw the moon towards the ecliptic. SepPrecession noctial points, with its equations, arising from the nutaof the equi

this force to be such that it would draw the moon

pose Roctial

tion of the earth's axis as a physical phenomenon, and down from Ni to i in the time ibat she would have mopoints, &c. to endeavour to account for it upon those mechanical ved from M to 1, in the tangent to her orbit. By the

principles which have so happily explained all the other combination of these motions, the moon will desert hier phenomena of the celestial motions.

orbit, and describe the line Mr, which makes the diaObserva. This did not escape the penetrating eye of Sir Isaac gonal of the parallelogram; and if no farther action of tions of Newton; and he quickly found it to be a consequence, the son be supposed, she will describe another orbit Newton

and the most beautiful proof, of the universal gravitation Mdn', lying between the orbit MCD n and the eclip-
and others
on this sub of all matter to all matter; and there is no part of his tic, and she will come to the ecliptic, and pass tbrough

immortal work where his sagacity and fertility of re it in a point n', nearer to M than n is, which was the
source shine more conspicuously than in this investiga- former place of her descending node. By this change
tion. It must be acknowledged, however, that New- of orbit, the line EX will no longer be perpendicular to
ton's investigation is only a shrewd guess, founded on as it; but there will be another line E x, which will now
sumptions, of which it would be extremely difficult to be perpendicular to the new orbit. Also the moon,
demonstrate either the truth or falsity, and which requi moving from M to r, does not move as if she had come
red the genius of a Newton to pick out in such a com from the ascending node N, but from a point N lying
plication of abstruse circumstances. The subject has oc- beyond it; and the line of the nodes of the orbit in this
cupied the attention of the first mathematicians of Eu new position is N'n'. Also the angle MN n is less
rope since his time ; and is still considered as the most than the angle MNm.
curious and difficult of all mechanical problems. The Thus the nodes shift their places in a direction op-
most elaborate and accurate dissertations on the preces posite to that of her motion, or move to the restward ;
sion of the equinoxes are those of Sylvabella and Walme the axis of the orbit changes its position, and the orbit
sly, in the Philosophical Transactions, published about itself changes its inclination to the ecliptic. These
the year 1754;. that of Thomas Simpson, published in momentary cbanges are diferent in different parts of
his Miscellaneous Tracts; that of Father Frisius, in the the orbit, according to the position of the line of the
Memoirs of the Berlin Academy, and afterwards with nodes. Sometimes the inclination of the orbit is in-
great improvements, in his Cosmograpbia ; that of Eu- creased, and sometimes the nodes move to the eastward.
ler in the Memoirs of Berlin ; that of D'Alembert in But, in general, the inclination increases from the time
a separate dissertation ; and that of De la Grange on that the nodes are in the line of syzigee, till they get into
the Libration of the Moon, which obtained the prize in quadrature, after which it diminislies till the nodes are
the Academy of Paris in 1769. We think the disserta- again in syzigee. The nodes advance only while they
tion of Father Frisius the most perspicuous of them all, are in the octants after the quadratures, and while the
being conducted in the method of geometrical analysis ; moon passes from quadrature to the node, and they re-
whereas most of the others proceed in the fluxionary cede in all other situations. Therefore the recess ex.
and symbolic method, which is frequently deficient in ceeds the advance in every revolution of the moon round
distinct notions of the quantities under consideration, the earth, and, on the whole, they recede.
and therefore does not give us the same perspicuous What has been said of one moon, would be true of
conviction of the truth of the results. In a work like each of a continued ring of moons surrounding the
ours, it is impossible to do justice to the problem, with earth, and they would thus compose a flexible ring,
out entering into a detail which would be thought ex which would never be flat but waved, according to the
tremely disproportioned to the subject by the genera- difference (both in kind and degree) of the disturbing
lity of our readers. Yet those who have the necessary forces acting on its different parts. But suppose these
preparation of mathematical knowledge, and wish to un moons to cohere, and to form a rigid and flat ring, na-
derstand the subject fully, will find enough here to give thing would remain in this ring but the excess of the con-

distinct notion of it; and in the article Ro. trary tendencies of its different parts. Its axis would be TATION, they will find the fundamental theorems, which perpendicular to its plane, and its position in any moment will enable them to carry on the investigation. We will be the mean position of all the axes of the orbits of shall first give a short sketch of Newton's investigation, each part of the flexible ring ; therefore the nodes of which is of the most palpable and popular kind, and is this rigid ring will continually recede, except when the highly valuable, not only for its ingenuity, but also be- plane of the ring passes through the sun, that is, when cause it will give our unlearned readers distinct and sa the nodes are in syzigee; and (says Newton) the motisfactory conceptions of the chief circumstances of the tion of these nodes will be the same with the mean mowhole phenomena.

tion of the nodes of the orbit of one moon. Sketch of

The incliNewton's Let S (6g. 2.) be the sun, E the earth, and M the nation of this ring to the ecliptic will be equal to the investiga moon, moving in the orbit NMCD n, which cuts the mean inclination of the moon's orbit during any one nion of it. plane of the ecliptic in the line of the nodes N revolution which has the same situation of the nodes. Fig. 2. has one balf raised above it, as represented in the figure, It will therefore be least of all when the nodes are in

the other half being hid below the ecliptic. Sup- quadrature, and will increase till they are in syzigee, pose

this orbit folded down; it will coincide with the and then diminish till they are again in quadrature. ecliptic in the circle N mcdn. Let EX represent the Suppose this ring to contract in dimensions, the disaxis of this orbit, perpendicular to its plane, and there. turbing forces will diminish in the same proportion, and fore inclined to the ecliptic. Since the moon gravi- in this proportion will all their effects diminish. Sup.

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