ee or me te et eee Pe ey 
826 
the centre of the system; to give motion 
to the earth, which the senses declared to 
be immoveable; to oppose the prevailmg 
opinion of between five and six thousand 
years ; to contradict the reputed truths 
of revelation; these were obstacles that 
required a most ardent mind to sur- 
mount; and we may rather wonder that 
Copernicus, a man, of ‘science, more at- 
tached to his study than to the world, 
should venture to permit his name to be 
attached to such heterodox sentiments, 
Death prevented him from suffering any 
evil consequences from his doctrine; and 
it perhaps was favourable,to his reputa- 
tion that his book could silently insinuate 
among the chosen few those notions 
which must have offended the great and 
little vulgar of thosé-times, and brought 
upon the author the censures and punish- 
ments of the church. 
. There were dificulties,also in his sys- 
tem which even were too pyeat for some 
real astronomers to surmountyand these, 
added to ancient prejudice, gave birth to 
the system introduced by ''ycho Brahe. 
He perceived clearly that the,Ptoletmaic 
system could no longer be maintained; but 
he was not prepared to dismiss the earth 
from its ancient station. . The. circular 
motion embraced by. Copernicus served 
to keep him/in his etrors; but his nume- 
rous observations were particularly be- 
neficial to science, and prepared the way 
for the calculations of Kepler, by which 
a new theory was to be established, 
Kepler adopted the,Copernican sys- 
tem, and in the year 1600 had the benefit 
of enjoying the society, of Tycho Brahe, 
at Prague, in Bohemia. Fortunately the 
Dane was then employed in observations 
on Mars, with a view to verify its ap- 
proaching opposition|in the sign.of Leo; 
and. the degree, of excentricity of this 
planet was a great. advantage in disco- 
vering the nature of-its orbit. Here the 
opposition between his and:his patron’s 
sentiments,led,to,a, most, laborious, exa- 
mination of ‘ancient tables, and calcula- 
tions from;thema ;and the inclination of 
the orbit, after repeated failures and 
many injurious methods, was at length 
discovered by him to be inyariable ; and 
after farther most laborious. efforts, to 
make his observatigns correspond with a 
circular.motion, he found them ineffec- 
tual, and was reduced to the necessity of 
looking out for some other theory. 
he labour employed by Kepler in en- 
deayouring to preserve the, motion of 
Mars in:a circle, is almost incredible, and 
Ea 
MATHEMATICS AND NATURAL PHILOSOPHY. 
the astronomer will appreciate it who 
gives himselfthe trouble of considering 
only the time employed in a few of the 
calculations which this work contains. 
From the suspicion that the orbit might 
not be circular to the conviction that it 
was not so, neither the time nor the pro- 
gresses were so Jong as ip previous at- 
tempts; yet within this time he had given 
up his first idea of calculating areas, and 
might have been lost in the fabyrindh of 
his calculations, if he had not discovered 
the distances in a circular orbit to be 
totally inconsistent with those deduced 
from observation. 
But much was to be done before his 
mind was satisfied, and the necessary 
steps to obtain this conviction are clearly 
pointed out; and after all, accident led 
the way to the great discovery, which 
was the foundation both of Kepler’s and 
of Newton’s fame. He had discovered 
that the breadth of the lunula, cut of by 
the real orbit of Mars from the exeentric, 
was but half of that cut off by the oval; 
and.that even at 90° from the apsides, 
where it was greatest, it did not exceed 
660 parts of a semi-diameter, or 152350. 
His disappointment here was great; but 
fortunately for him whilst he was con- 
templating tke subject, it occurred to him 
that these 660 parts were equak to 432 
parts of a semi-diameter 100000, that is 
nearly to 429 the haif of 858, which he 
had found to be in the same.parts the ex. 
treme breadth of the lunula, cutoff in 
the oval theory;and turning his attentioa 
to the greatest optical equation of Mars, 
whichis between 5° 18’, and 5° 19’, he 
perceived that 429 was also the excess, cf 
the scecant of 5°,.18'. above the radivs 
100000. Here new light broke in upcn 
him ;, he pursued. it with ardour ; the 
circular motion was given up for the d- 
liptical, not without extreme. perplexity, 
and. ‘* almost approaching to derangement of 
mind;”’ and he was occupied in the famous 
problem afterwards called the Keplerian, 
from the mean anomaly to find the true, 
or, by a line drawn from the focus, to dis 
vide a.semi.ellipse in any given ratio. | 
Nothing but the utmost ardour for 
science, indefatigable industry, and per- 
fect knowledge of. figures, could have 
enabled the. discoverer of the facts rela. 
tive to the planetary system, to ascertais 
that the planets moved in elliptical or 
bits, described equal, areas around tle 
sun in equal times, and that the squars. 
of their periodical times varied as te 
. . 4 
cubes of their mean distances from ws 
. 
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