ASTRONOMY. 
373 
Chrift, found that the longittides of the dars in his time 
were greater than they had been before obferved by 'ly- 
mochares, and than they were in the fphere of Eudoxus, 
who wrote 380 years before Chrift. Ptolemy alfo percei¬ 
ved the gradual change in the longitudes of the ftars; but 
lie dated the quantity at too little, making it but one de¬ 
gree in 100 years, which is at the rate only of 36" per 
year. Y-hatfg, a Chinefe, in the year 721, dated the 
quantity of this change at one degree in eighty-three years, 
which is at the rate of 435'' per year. Other more modern 
adronomers have made this precedion dill more, but with 
fome fmall differences from each other ; and it is now ufu- 
ally taken at 50^" per year. All thefe rates are deduced 
from a comparifon of the longitude of certain dars as ob. 
ferved by more ancient adronomers, with the later obfer- 
vations of the fame dars, viz. by fubtrafting the former 
from the latter, and dividing the remainder by the num¬ 
ber of years in the interval between the dates of the ob- 
fervations. Thus, by a medium of a great number of 
comparifons, the quantity of the annual change has been 
fixed at 50%", according to which rate it will require 25791 
years for the equinoxes to make their revolution wedward 
quite round the circle, and return to the fame point again. 
Thus, by taking the longitudes of the principal ftars 
edablidted by Tycho Brahe, for the beginning of 1586, 
and comparing them with the fame 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 feveral dars, viz. 
7 
Arietatis 
2 ° 
n' 
37 
Aldebaran 
- 0 2 
17 
45 
f* 
Geminorum 
~ 2 
17 
I 
13 
Geminorum 
- 2 
15 
26 
Regulus 
« 2 
l6 
32 
a 
Virginis 
2 
18 
18 
a 
Aquilae 
2 
19 
I 
CL 
Pegati 
- N 2 
l6 
12 
& 
Librte - 
- 2 
17 
52 
Antares 1 
2 
l6 
28 
E 
Tauri 
- 2 
17 
58 
7 
Geminorum 
-» 2 
18 
38 
7 
Cancri 
- 2 
19 
12 
7 
Leonis - 
- 2 
1 9 
38 
7 
Capricorni 
- 2 
l6 
IO 
Medium of thefe fifteen ftars - 2 17 35 
it 
Which divided by 164, the interval of years, gives 50'336", 
or nearly 505", or after the rate of i° 23' 53!" in 100 
years, or 25,748 years for the whole revolution, or circle 
of 36c degrees. And nearly the fame conclufion refults 
from the longitudes of the dars in the Britannic catalogue, 
compared with thofe of dill later catalogues. 
The ancients, and even fome of the moderns, have ta¬ 
ken the equinoxes to be immoveable ; and aferibed that 
change in the didance of the dars from it, to a real motion 
of the orb of fixed dars, which they fuppofed had a (low 
revolution about the poles of the ecliptic ; fo as that all 
the dars perform their circuits in the ecliptic, or its paral¬ 
lels, in the fpace of 25,791 years; after which they fhould 
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 fird, 
and all things come round in the fame order as they have 
done before. 
The phenomena of this retrograde motion of the equi¬ 
noxes, or interfe&ions of the equino&ial ivith the ecliptic, 
and confequently of the conical motion of the Earth’s axis, 
by which the pole of the equator deferibes a fmall circle 
in the fame period of time, may be underdood and illuf- 
trated by a fcheme, as follows: Let NZSVL be the Earth, 
SON A its axis produced to the darry heavens, and termi¬ 
nating in A, the prefent north pole of the heavens, which 
is vertical to N, the north pole of the Earth. Let EOQ^ 
be the equator, T«sZ the tropic of Cancer, and VTy? 
Vol. 11. No. 77 . 
the tropic of Capricorn; VOZ the ecliptic, and BO its 
axis, both of which are immoveable among the dars. But, 
as the equinodlial points recede in the ecliptic, the Earth’s 
axis SON is in motion upon the Earth’s centre: O, in fuch 
a manner as to deferibe the double cone NOa and SOr, 
round the axis of the ecliptic BO, in the time that the 
equinodtial points move round the ecliptic, which is 25,791 
years; and, in that length of time, the north pole of the 
Earthls axis, produced, deferibes the circle ABCDA in 
the darry heavens, round the pole of the ecliptic, which 
keeps immoveable in the centre of that circle. The Earth’s 
axis being now 23 0 28' inclined to the axis of the ecliptic, 
the circle ABCDA, deferibed by the north pole of the 
Earth’s axis produced to A, is 46° 56' in diameter, or dou¬ 
ble the inclination of the Earth’s axis. In confequenee 
of this, the point A, which is at prefent the north pole of 
the heavens, and near to a dar of the fecond magnitude in 
the end of the Little Bear’s Tail, mud be deferted by the 
Earth’s axis; which moving backwards one degree every 
711 years nearly, will be directed towards the dar or point 
B in 6447! years hence ; and in double of that time, or 
in 12,895! years, it will be directed towards the dar or 
point C ; which will then be the north pole of the heavens, 
although it is at prefent 8J degrees fouth of the zenith of 
London L. The prefent pofition of the equator EOCVwill 
then be changed to cOq, the tropic of Cancer TffiZ into 
V/25, and the tropic of Capricorn VTvf into tVfZ; as is 
evident by the figure. And the Sun, in the fame part of 
the heavens where he is now over the earthly tropic of 
Capricorn, and makes the diorted days and longed nights 
in the northern hemifphere, w ill then be over the earthly 
tropic of Cancer, and make the days longed and the nights 
diorted. So that it will require 12,895! years yet more, 
or from that time, to bring the north pole N quite round, 
fo as to be directed toward that point of the heavens which 
is vertical to it at prefent. And then, and not till then, 
the fame dars which at prefent deferibe the equator, tro¬ 
pics, and polar circles, &c. by the Earth’s diurnal motion, 
will deferibe them over again. 
From this fiiifting of the equinoctial points, and with 
them all the figns of the ecliptic, it follows, that thofe 
dars which in the infancy of adronomy were in Aries, are 
now found in Taurus; thofe of Taurus in Gemini, &c. 
Hence likewife it is, that the dars which rofe or fet at any 
particular feafon of the year, in the times of Kefiod, Eu¬ 
doxus, Virgil, Pliny, by no means anfwer at this time to 
their deferiptions. 
As to the phyfical caufe of the precedion of the equi¬ 
noxes, Sir Ifaac Newton demonftrates, that it arifes from 
the broad or flat fpheroidical figure of the Earth ; which 
itfelf arifes from the Earth’s rotation about its axis: for, 
as more matter has thus been accumulated all round the 
equatorial parts than any where elfe on the Earth, the Sun 
and Moon, when on either fide of the equator, by attract¬ 
ing this redundant matter, bring the equator fooner under 
them, in every return towards it, than if there was no 
fuch accumulation. Sir Ifaac Newton in determining the 
S C quantity 
