333 ASTRO 
invented his fydem. Since th« calculations of Kepler, 
. therefore, overturned what Copernicus had principally in 
view in edablilhing his fydem, we cannot wonder that 
they Ihould at fird feem rather to embarrafs than im¬ 
prove it. 
It is true, by thele elliptical orbits and unequal mo¬ 
tions, Kepler difengaged the fyflem from the embarralT- 
ment of thofe fmall epicycles, which Copernicus, in order 
to connect the feemingly accelerated and retarded move¬ 
ments of the planets with their fuppofed real equality, 
had been obliged to leave in it. For it is remarkable, that 
though Copernicus had delivered the orbits of the planets 
from the enormous epicycles of Hipparchus, that though 
in this conlifted the great fuperiority of-his fyflem above 
that of the ancient aftronomers, he was yet obliged him- 
felf to abandon in home meafure this advantage, and to 
make ufe of fome fmall epicycles to join together thofe 
Teeming irregularities. His epicycles indeed, like the ir¬ 
regularities for whole fake they were introduced, were but 
fmall ones, and the imaginations of his firth followers feem 
accordingly, either to have flurred them over altogether, 
or fcarcely* to have obferved them. Neither Galileo nor 
Gadendi, the two mod eloquent of his defenders, take any 
notice of them. Nor does it feem to have been generally 
attended to, that there was any fuch thing as epicycles in 
the fyllem of Copernicus, till Kepler, in order to vindi¬ 
cate his own elliptical orbits, infilled, that, even accord¬ 
ing to Copernicus, the body of the planet was to be found 
but at two different places in the circumference of that 
circle which the centre of its epicycle deferibed. 
It is alfo true that an ellipfe is, of all curve lines after 
a circle, the fimplelt and mod ealily conceived; and it is 
true, beddes all this, that while Kepler took from the 
motion of the planets the eadelt of all proportions, that of 
equality, he did not leave them abfolutely without one, 
but afeertained the rule by which their velocities continu¬ 
ally varied ; for a genius fo fond of analogies, when he 
had taken away one, would be fure to fubditute another 
an its room. Notwithdanding all this, notwithdanding 
that his fydem was better fupported by obfervations than 
any fydem had ever been before, yet fuch was the attach- 
ynenpto the equal motions and circular orbits of the pla¬ 
nets, that it feems for fome time to have been in general 
but little attended to by the learned, to have been alto¬ 
gether neglected by philofophers, and not much regarded 
even by adronomers. 
Gadendi, who began to figure in the world about the 
latter days of Kepler, and w ho was himfelf no mean adro- 
noaier, feems indeed to have conceived a good deal of 
elteem for his diligence and accuracy, in accommodating 
the obfervations of Tycho Brahe to the fydem of Coper¬ 
nicus. But Gadendi appears to have had no comprehen- 
fion of the importance of thofe alterations which Kepler 
had made in that fydem, as is evident from his fcarcely 
ever mentioning them in the whole courfe of his volumi¬ 
nous writings upon adronomy. Des Cartes, the cotempo- 
rarv and rival of Gadendi, feems to have paid no attention 
to them at all, but to have built his theory of the heavens 
without any regard to them. Even thofe adronomers, 
whom a ferious attention had convinced of the judnefs of 
his correftions, were dill fo enamoured with the circular 
orbits and equal motions, that they endeavoured to com¬ 
pound his fydem with thofe ancient but natural preju¬ 
dices. Thus Ward endeavoured to fhew, that though the 
planets moved in elliptical orbits, which had the Sun in 
one of their foci, and though their velocities in the ellip¬ 
tical line were continually varying, yet if a ray was fup- 
poled to be extended from the centre of any one of them 
to the other focus, and to be carried along by the periodi¬ 
cal motion of the planet, it would make equal angles in 
equal times, and confequently cut off equal portions of the 
circle of which that other focus was the centre. To one 
therefore, placed in that focus, the motion of the planet 
would appear to be perfeiSfly circular and perfectly equable, 
in the fame manner as in the equalizing circles of Ptolemy 
N O M Y. 
and Hipparchus. Thus Bouillaud, who cenfured this hypo* 
thefis of Ward, invented another of the fame kind, infi¬ 
nitely more whimfical and capricious. The planets, ac¬ 
cording to that afironomer, always revolve in circles ; for, 
that being the mod perfect figure, it is impoilible they 
fhould revolve in any other. No one of them however 
continues to move in any one circle, but is perpetually 
pading from one to another, through an infinite number of 
circles, in the courfe of each revolution ; for an ellipfe, 
faid he, is an oblique lection of a cone, and in a cone, be¬ 
twixt the two vortices of the ellipfe there is an infinite 
number of circles, out of the infinitely fmall portions of 
which the elliptical line is compounded. The planet there¬ 
fore, which moves in this line, is, in every point of it, 
moving in an infinitely fmall portion of a certain circle. 
The motion of each planet too, according to him, was 
necedarily for the fame reafon perfectly equable, an equa¬ 
ble motion being the mod perfect of all motions. It was 
not however, in the elliptical line, that it was equable, 
but in any one. of the circles that were parallel to the bale 
of that cone, by whole feCtion this elliptical line had been 
formed : for, if a ray was extended from the planet to any 
one of thofe circles, and carried along by its periodical 
motion, it would cut oft’ equal portions of that circle in 
equal times ; another mod fantadical equalizing circle, 
fupported by no other foundation befides the frivolous 
connection betwixt a cone and an ellipfe, and recommended 
by nothing but the natural padion for circular orbits and 
equable motions. It may be regarded as the lad effort of this 
padion, and may ferve to disw the force of that principle 
which could thus oblige this accurate obferver, and great 
improver of the theory of the heavens, to adopt fo drange 
an hypothefis. Such was the difficulty and hedtation with 
which the followers of Copernicus adopted the corrections 
or Kepler. The rule indeed which Kepler afeertained 
for determining the gradual acceleration cr retardation in 
the movement of the planets, was intricate, and difficult 
to be comprehended; it could therefore but little facili¬ 
tate the progrefs of the imagination in tracing thofe revo¬ 
lutions which were fuppofed to be conducted by it. Ac¬ 
cording to that adronomer, if a llraight line was drawn 
from the centre of each planet to the Sun, and carried 
along by the periodical motion of the planet, it would 
defcribe equal areas in equal times, though the planet did 
not pals over equal fpaces ; and the fame rule he found 
took place nearly with regard to the Moon. The imagi¬ 
nation, when acquainted with the law by which any motion 
is accelerated or retarded, can follow and attend to it more 
eafily, than when at a lofs, and as it were wandering in 
uncertainty with regard to the proportion which regulates 
its varieties; the difeovery of this analogy therefore, no 
doubt, rendered the fydem of Kepler more agreeable to 
the natural tade of mankind : it was, however, an analogy 
too difficult to be followed or comprehended, to render 
it completely fo. 
Kepler, beddes this, introduced another new analogy 
into the fydem, and fird difeovered, that there was one 
uniform relation obferved betwixt the didances of the Pla¬ 
nets from the Sun, and the times employed in their peri¬ 
odical motions. He found, that their periodical times 
were greater than in proportion to their didances, and lefs 
than in proportion to the fquares of thole didances ; but, 
that they were nearly as the mean proportionals betwixt their 
didances and the fquares of their didances; or, in other 
words, that the fquares of their periodical times were 
nearly as the cubes of their didances ; an analogy, w hich, 
though, like all others, it no doubt rendered the fydem 
fomewhat more dillinct and comprehendble, was, however, 
as well as the former, of too intricate a nature to facilitate 
very much the effort of the imagination in conceiving it. 
The truth of thefe analogies, however, intricate as they 
were, was at lad fully edablidied by the obfervations of 
Cafiini. That adronomer fird difeovered, that the fecon- 
dary planets of Jupiter and Saturn revolved round their 
primary ones, according to the fame laws which Kepler 
