3 7 4 ASTRO 
quantity of the annual precefiion from the theory of gra¬ 
vity, on fuppofition that the equatorial diameter of the 
Earth is to the polar diameter as 230 to 229, finds the - 
Sun’s action. fufficient to produce a precellion of 9.4" only; 
and, collecting from the tides the proportion between the 
Sun’s force and the Moon’s to be as 1 to 4§, he fettles the 
mean precefiion, refulting from their joint actions, at 50"; 
which, its muff be owned, is nearly the fame as it has fince 
been found by the belt obfervations; and yet feveral other 
mathematicians have fince objected to the truth of Sir 
Ifaac Newton’s computation. Indeed, to determine the 
quantity of the precefiion arifing from tire aCtion of the 
Sun, is a problem that has been much agitated among mo¬ 
dern mathematicians ; and, although they feemto agree as 
to Newton’s.miftake in the folution- of it, they have yet 
generally difagreed from one another. M. d’Alembert, 
In 1749, printed a treatife on this fubjefl, and claims the 
honour of having been the frrft who rightly determined 
the method of refolving problems of this kind. Thefub- 
je6f has been alfo confidered by Euler, Frifius, Silvabelle, 
Waltpelley, Simpfon, Emerfon, La Place, La Grange, Lan- 
den, Milner, and Vince. 
M. Silvabelle, (fating the ratio of the Earth’s axis to 
be that of 178 to 177, makes the annual precefiion caufed 
by the Sun 13" 52."', and that of the Moon 34" 17"'; ma¬ 
king the ratio of the lunar force to the folar to be that of 
3 to 2 ; alfo the nutation of the Earth’s axis caufed by the 
Moon, during the time of a femi-revolution of the pole 
of the Moon’s orbit, i. e. in 9! years, lie makes 17" 51"'. 
M. Walmefiey, on the fuppofition that the ratio of the 
Earth’s diameters is that of 230 to 229, and the obliquity 
of the ecliptic to the equator 23 0 28' 30", makes the an¬ 
nual precefiion, owing to the Sun’s force, equal to 10-383"; 
but, fuppofing the ratio of the diameters to be that of 178 
to 177, that precefiion will be 13-67 5". Mr. Simpfon, by 
a different method of calculation, determines the whole 
annual precefiion of the equinoxes, caufed by the Sun, at 
21" 6"'g and he has pointed out the errors of the compu¬ 
tations propofed by M. Silvabelle and M, Walmefiey. 
Mr. Milner’s deduction agrees with that of Mr. Simpfon, 
as well as Mr. Vince’s; and their papers contain befides 
feveral curious particulars relative to this fubjeCt. 
As to the effeCt of the planets upon the equinoctial 
points, M. de la Place, in his new researches on this ar¬ 
ticle, finds that their aCtion caufes thofe 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 hmi-folar precefiion mult be 50-4349", fince the total 
obferved precefiion is 50J", or 50-25". 
Tofind the Precejfi.cn in right aficeenfion and declination .—Put 
t(— the declination of a ftar, and a— its right afcenfion ; 
then their annual variations of precefllons will be nearly as 
follow, viz. 
20-084" X cof. a— the annual precef. in declinat. 
And 46-0619"-!- 20-084" X fm- a X tang, d — that of 
right afcenfion. See the Connoiffance des Temps for 1792, 
p. 206, &c. 
Of the Obliquity of the Ecliptic. 
The ecliptic is a great circle of the fphere conceived to 
pafs through the middle of the zodiac. It js fometimes 
called the via Solis, or ‘Sun’s path,’ being the track which 
he appears to defcribe among the fixed (tars; though more 
properly it is the apparent path of the Earth, as viewed 
from the Sun, and thence called the heliocentric circle of 
the Earth. It is called the ecliptic, becaufe all the eclip- 
fes of the Sun or Moon happen when the Moon erodes it, 
or is nearly in one of thofe two parts of her orbit where 
it erodes the ecliptic, which points are the Moon’s nodes. 
Upon the ecliptic are marked and counted the twelve ce- 
lellial figns, Aries, Taurus, Gemini, &c. and upon it is 
counted the longitude of the planets and liars. It is pla¬ 
ced obliquely with refpeft to the equator, which it cuts 
m two oppofite points, viz. the beginning of Aries and 
Libra, which are directly oppofite to each other, andcall- 
N O M Y. 
ed the equinoxes, making the one-half of the ecliptic t» 
the north, and the other half on the fouth fide of the equa¬ 
tor ; the two extreme points of it, to the north and fouth,- 
which are oppofite to each other, and at a quadrant dif- 
tance from the equinoctial points both ways, are called the 
folftices, or folftitial points, or alfo the two tropics, which 
are at the beginning of Cancer and Capricorn, and which, 
are at the fartheft difiance of any points of it from the 
equator, which diflance is the me a hire of the Sun’s great- 
eft declination, which is the fame with the obliquity of the 
ecliptic, or the angle it makes with the equator. 
This obliquity, of the ecliptic is not permanent, but is 
continually diminilhing, by the ecliptic approaching near¬ 
er and nearer to a parallelifm with the equator, at the rate 
of half a fecond in a year nearly, or from 50'.' to 55" ini 
100 years, as is deduced from ancient and modern obfer¬ 
vations compared together; and as the mean obliquity c£ 
the ecliptic was 23 0 28' about the end of the year 178.8, or 
beginning of 1789, by adding half a fecond for each pre¬ 
ceding year, or fubtracling the fame for each following; 
year, the mean obliquity will be found nearly for any year 
either before or fince that period. The quantity however- 
of this change is varioufly dated by different authors, from. 
50" to 60" or 70" for each century or 100 years. Hippar¬ 
chus, almoft two thoufand years fince, obferved the obli¬ 
quity of the ecliptic, and found it about 23? 51'; and alt 
fucceeding aftronomers, to the prefent time, having ob¬ 
ferved the fame, have found it always lefsandlefs; being 
now rather under 23 0 28'; a difference of about 23'. in 195a 
years; which gives a medium of 70" in 100years. There 
is reafon however to think that the diminution is vari¬ 
able. 
This diminution of the obliquity of the ecliptic to the 
equator, according to Mr. Long and fome others, is chief¬ 
ly owing to the unequal attraflion of the Sun and Moon > 
on the protuberant matter about the Earth’s equator. For. 
if it be confidered, fay they, that the Earth is not a'per- 
fe6t fphere, but an oblate fpberoid, having its axis ihort- 
er than its equatorial diameter; and that the Sun and Moon 
are conftantly acting obliquely upon the greater quantity 
©f matter about the equator, drawing it, as it were,- to¬ 
wards a nearer and nearer coincidence with the ecliptic ; 
it will not appear ftrange that thefe actions ffmuld gradu¬ 
ally diminifh the angle between the planes of thofe two cir¬ 
cles. Nor is it lefs probable that the mutual attractions 
of all the planets (hould have a tendency to bring their or¬ 
bits to a coincidence: though this change is too fmall to 
become fenlible in many ages. It is now however well? 
known, that this change in the obliquity of the ecliptic is. 
wholly owing to the actions of the planets upon the Earth, 
and especially the planets Venus and Jupiter, but chiefly 
the former. See La Grange’s excellent paper upon this 
fubject in the Memoirs of the French Academy for 1774; 
Cafiini’s in 1778; and La Lande’s Aftron. vol. iii. Ac¬ 
cording to La Grange, who proceeds upon theory, the an-- 
nual change of obliquity is variable, and has its limits : 
about 2000 years ago, he thinks it was after the rate of. 
about 38" in 100 years; that it is now, and will be for 400. 
years to come, 56" per century; but 2000 years hence, 
49" per century. According to Caflini, who computes 
from obfervations of the obliquity between the years 1739 
and 1778, the annual change.at prefent is 60" or 1' in 100 
years. But according to La Lande, the diminution is at 
the rate of 88" per century; while Dr. Malkelyne makes 
it only 50" in the fame time. 
Befides the regular diminution of the obliquity of the 
ecliptic, at the rate of near 50" in a century, or half a fe¬ 
cond a year, which arifes from a change of the ecliptic 
itfelf, it is fubjeiSl to two periodical inequalities, the one 
produced by the unequal force of the Sun in caufing the 
precefiion of the equinoxes, and the other depending 011 
the nutation of the Earth’s axis. See the Explanation and 
Ufe of Dr. Mafkelyne’s Tables and Obfervations, p. 6, 
where we are fhewn how to calculate thofe inequalities, 
and where he (hews that, from his own obfervations, the 
mean 
