35 o ASTRO 
to and Ariftotle, and with the regularity and harmony of 
their fyftem, in itfelf perfe£lly beautiful, though it cor- 
refpotids but inaccurately with the phenomena, endeavour¬ 
ed to revive this-ancient aftronomy, which had long given 
place to that of Ptolemy and Hipparchus, he found it ne- 
ceffary ta multiply the number of celeflial fpheres to fe- 
venty-two; neither were all thefe enough. 
This fyftem had now become as intricate and complex 
as thofe appearances themfelves, which it had been invent¬ 
ed to render uniform and coherent. The imagination, 
therefore, found itfelf but little relieved from that embar- 
raffment, into which thofe appearances had thrown it, by 
fo perplexed an account of things. Another fyftem, for 
this reafon, not long after the days of Ariftotle, was in¬ 
vented by Apollonius, which was afterwards perfefled by 
Hipparchus, and delivered to us by Ptolemy, the more 
artificial fyftem of eccentric fpheres and epicycles. 
In this fyftem, they firft diftinguillied betwixt the real 
and apparent motion of the heavenly bodies. Thefe, they 
obferved, upon account of their immenfe diftance, mull 
neceftarily appear to revolve in circles concentric with the 
globe of the Earth, and with one another: but that we 
cannot, therefore, be certain that they really revolve in 
fuch circles, fince, though they did not, they would ftiU 
have the fame appearance. By fuppofing, therefore, that 
the Sun and the other planets revolved in circles, whofe 
centres were very diftant from the centre of the Earth ; 
that confcquently, in the progrefsof their revolution, they 
mull fometimes approach nearer, and fometimes recede 
farther from it, and muft, therefore, to its inhabitants, ap¬ 
pear to move fafter in the one cafe and flower in the other; 
thofe philofophers imagined they could account for the ap¬ 
parently unequal velocities of all thofe bodies. 
By fuppofing, that, in the folidity of the fphere of each 
of the five planets there was formed another little fphere, 
called an epkycle, which revolved round its own centre, at 
the fame time that it was carried round the centre of the 
Earth by the revolution of the great fphere, betwixt whofe 
concave and convex fides it was enclofed ; in the fame man¬ 
ner as we might fuppofe a little wheel inclofed within the 
outer circle of a great wheel, and which whirled about 
feveral times upon its own axis, while its centre was car¬ 
ried round the axis of the great wheel; they imagined 
they could account for the retrograde and flationary ap¬ 
pearances of thofe molt irregular objects in the heavens. 
The planet, they fuppofed, was attached to the circumfe¬ 
rence, and whirled round the centre of this little fphere, 
at the fame time that it was carried round the Earth by 
the movement of the great fphere. The revolution of 
this little fphere, or epicycle, was fuch, that the planet, 
when in the upper part of it, that is, when fartheft oft 
and leaft fenfible to the eye, was carried round in the fame 
direction with the centre of the epicycle, or with the fphere 
in which the epicycle was inclofed ; but, when in the low¬ 
er part, that is, when neareft and moft fenfible to the eye, 
it was carried round in a direction contrary to that of the 
centre of the epicycle : in the fame manner as every point 
in the upper part of the outer circle of a coach-wheel re¬ 
volves forward in the fame direttion with the axis, while 
every point in the lower part revolves backwards in a con¬ 
trary direction to the axis. The motions of the planet, 
therefore, fnrveycd from the Earth, appeared diredt when 
in the upper part of the epicycle, and retrograde when 
in the lower. When again it either defcended from the 
upper part to the lower, or afcended from the lower to the 
upper, it neceftarily appeared ftationary. 
But, though, by the eccentricity of the great fphere, 
they were thus able,, in fome meafure, to connect toge¬ 
ther the unequal velocities of the heavenly bodies, and, by 
the revolutions or the iittle fphere,. the direct, ftationary, 
and retrograde, appearances of the planets, there was ano¬ 
ther difficulty that ftill remained. Neither the Moon, nor 
the three fuperior planets, appear always in the fame part 
of the heavens when at their periods of moft retarded mo¬ 
tion, or when they are fuppofed to be a! thegrcatcft diftance 
% 
N O M y. 
from the Earth. The apogeum, therefore, or the point 
of the greateft diftance from the earth, in the fpheres of 
each of thofe bodies, muft have a movement of its own, 
which may carry it fucceflively through all the different 
points of the ecliptic. They fuppofed, therefore, that, 
while the great eccentric fphere revolved eaftwards round 
itfr centre, its centre too revolved weftwards in a cir¬ 
cle of its own, round the centre of the earth, and thus 
carried its apogeum through all the different points of the 
ecliptic. 
But, with all thofe combined and perplexed circles, tho’ 
the patrons of this fyftem were able to give fome degree 
of uniformity to the real directions of the planets, they 
found it impoflible fo to adjuft the velocities of thofe lup- 
pofed fpheres to the phenomena, as that the revolution of 
any one of them, when furveyed from its own centre, 
ffiould appear perfectly equable and uniform. From that 
point, the only point in which the velocity of what moves 
in a circle can be truly judged of, they would ftill appear 
irregular and inconftant, and fuch as tended to embarrafs 
and confound the imagination. They invented, therefore, 
for each of them, a new circle, called the equalizing circle y 
from whofe centre they fhould all appear perfectly equa¬ 
ble ; that is, they fo adjufted the velocities of thefe fpheres, 
as that, though the revolution of each of them would ap¬ 
pear irregular when furveyed from its own centre, there 
fhould, however, be a point comprehended within its cir¬ 
cumference, from whence its motions fliould appear to cut 
off, in equal times, equal portions of the circle, of which 
that point was the centre. 
Nothing can more evidently fhew how much the repofe 
and tranquillity of the imagination is the ultimate end of 
philofophy, than the invention of this equalizing circle. 
The motions of the heavenly bodies had appeared incon¬ 
ftant and irregular, both in their velocities and in their di¬ 
rections. They were fuch, therefore, as tended to embar¬ 
rafs and confound the imagination, whenever it attempted 
to trace them. The invention of eccentric fpheres, of 
epicycles, and of the revolution of the centres of the ec¬ 
centric fpheres, tended to allay this confufion, to connect 
together thofe disjointed appearance', and to introduce 
harmony and order into the mind’s conception of the move¬ 
ments of thofe bodies. It did this, however, but imper¬ 
fectly; it introduced uniformity and coherence into their 
real directions. But their velocities, when furveyed from 
the only point in which the velocity of what moves in a 
circle can be truly judged of, the centre of that circle ftill 
remained, in fome meafure, inconftant as before ; and ftill, 
therefore, embarralled the imagination. The mind found 
itfelf fomewhat relieved from this embarraflment, when it 
conceived, that, how irregular foever the motions of each 
of thofe circles might appear when furveyed from its own 
centre, there was, however, in each of them, a point, from 
whence its revolution would appear perfectly equable and 
uniform, and fuch as the imagination could ealily fellow. 
1 hole philofophers tranfported themfelves, in fancy, to 
the centres of thefe imaginary circles, and took pleafure 
in furveying from thence all thofe fantaftical motions, ar¬ 
ranged according to that harmony and order which it had 
been the end of all their refearches to beftow upon them. 
Here, at laft, they enjoyed that tranquillity and repofe 
which they had purfued through all the mazes of this in¬ 
tricate hypothesis; and here they beheld this, the moft 
beautiful and magnificent part of the great theatre of na¬ 
ture, fo difpofed and conftructed, that they could attend, 
with eafe and delight, to all the revolutions and changes 
that occurred in it. 
Thus, the fyftem of concentric, and that of eccentric, 
fpheres, f'eem to have been the two fyftems of aftronomy 
that had the moft credit and reputation with that part of 
the ancient world who applied themfelves particularly to 
the ftudy of the heavens. Cleanthes, however, and tire 
other philofophers of the Stoical feCt who came after him, 
appear to have had a fyftem of their own, quite different 
from cither. But, though jufily renowned for their Ik ill 
in 
