COPPERNICUS.
“But in this our age, one rare witte (seeing the continuall errors
that from time to time more and more continually have been discovered,
besides the infinite absurdities in their Theoricks, which they have
been forced to admit that would not confesse any Mobilitie in the
ball of the Earth) hath by long studye, paynfull practise, and rare
invention delivered a new Theorick or Model of the world, shewing
that the Earth resteth not in the Center of the whole world or globe
of elements, which encircled and enclosed in the Moone’s orbit, and
together with the whole globe of mortality is carried yearly round
about the Sunne, which like a king in the middest of all, rayneth and
giveth laws of motion to all the rest, sphaerically dispersing his
glorious beames of light through all this sacred coelestiall Temple.”
THOMAS DIGGES, 1590.
70. The growing interest in astronomy shewn by the work of such men as
Regiomontanus was one of the early results in the region of science
of the great movement of thought to different aspects of which are
given the names of Revival of Learning, Renaissance, and Reformation,
The movement may be regarded primarily as a general quickening of
intelligence and of interest in matters of thought and knowledge. The
invention of printing early in the 15th century, the stimulus to the
study of the Greek authors, due in part to the scholars who were driven
westwards after the capture of Constantinople by the Turks (1453), and
the discovery of America by Columbus in 1492, all helped on a movement
the beginning of which has to be looked for much earlier.
Every stimulus to the intelligence naturally brings with it a tendency
towards inquiry into opinions received through tradition and based
on some great authority. The effective discovery and the study of
Greek philosophers other than Aristotle naturally did much to shake
the supreme authority of that great philosopher, just as the Reformers
shook the authority of the Church by pointing out what they considered
to be inconsistencies between its doctrines and those of the Bible.
At first there was little avowed opposition to the principle that
truth was to be derived from some authority, rather than to be sought
independently by the light of reason; the new scholars replaced the
authority of Aristotle by that of Plato or of Greek and Roman antiquity
in general, and the religious Reformers replaced the Church by the
Bible. Naturally, however, the conflict between authorities produced
in some minds scepticism as to the principle of authority itself; when
freedom of judgment had to be exercised to the extent of deciding
between authorities, it was but a step further—a step, it is true, that
comparatively few took—to use the individual judgment on the matter at
issue itself.
In astronomy the conflict between authorities had already arisen,
partly in connection with certain divergencies between Ptolemy and
Aristotle, partly in connection with the various astronomical tables
which, though on substantially the same lines, differed in minor
points. The time was therefore ripe for some fundamental criticism of
the traditional astronomy, and for its reconstruction on a new basis.
Such a fundamental change was planned and worked out by the great
astronomer whose work has next to be considered.
71. _Nicholas_ Coppernic or _Coppernicus_[45] was born on February
19th, 1473, in a house still pointed out in the little trading town of
Thorn on the Vistula. Thorn now lies just within the eastern frontier
of the present kingdom of Prussia; in the time of Coppernicus it lay
in a region over which the King of Poland had some sort of suzerainty,
the precise nature of which was a continual subject of quarrel between
him, the citizens, and the order of Teutonic knights, who claimed a
good deal of the neighbouring country. The astronomer’s father (whose
name was most commonly written Koppernigk) was a merchant who came
to Thorn from Cracow, then the capital of Poland, in 1462. Whether
Coppernicus should be counted as a Pole or as a German is an intricate
question, over which his biographers have fought at great length and
with some acrimony, but which is not worth further discussion here.
Nicholas, after the death of his father in 1483, was under the care
of his uncle, Lucas Watzelrode, afterwards bishop of the neighbouring
diocese of Ermland, and was destined by him from a very early date for
an ecclesiastical career. He attended the school at Thorn, and at the
age of 17 entered the University of Cracow. Here he seems to have first
acquired (or shewn) a decided taste for astronomy and mathematics,
subjects in which he probably received help from Albert Brudzewski,
who had a great reputation as a learned and stimulating teacher; the
lecture lists of the University show that the comparatively modern
treatises of Purbach and Regiomontanus (chapter III., § 68) were the
standard textbooks used. Coppernicus had no intention of graduating at
Cracow, and probably left after three years (1494). During the next
year or two he lived partly at home, partly at his uncle’s palace at
Heilsberg, and spent some of the time in an unsuccessful candidature
for a canonry at Frauenburg, the cathedral city of his uncle’s diocese.
The next nine or ten years of his life (from 1496 to 1505 or 1506)
were devoted to studying in Italy, his stay there being broken only
by a short visit to Frauenburg in 1501. He worked chiefly at Bologna
and Padua, but graduated at Ferrara, and also spent some time at
Rome, where his astronomical knowledge evidently made a favourable
impression. Although he was supposed to be in Italy primarily with a
view to studying law and medicine, it is evident that much of his best
work was being put into mathematics and astronomy, while he also paid a
good deal of attention to Greek.
[Illustration: COPPERNICUS.]
During his absence he was appointed (about 1497) to a canonry at
Frauenburg, and at some uncertain date be also received a sinecure
ecclesiastical appointment at Breslau.
72. On returning to Frauenburg from Italy Coppernicus almost
immediately obtained fresh leave of absence, and joined his uncle
at Heilsberg, ostensibly as his medical adviser and really as his
companion.
It was probably during the quiet years spent at Heilsberg that he first
put into shape his new ideas about astronomy, and wrote the first draft
of his book. He kept the manuscript by him, revising and rewriting
from time to time, partly from a desire to make his work as perfect as
possible, partly from complete indifference to reputation, coupled with
dislike of the controversy to which the publication of his book would
almost certainly give rise. In 1509 he published at Cracow his first
book, a Latin translation of a set of Greek letters by Theophylactus,
interesting as being probably the first translation from the Greek ever
published in Poland or the adjacent districts. In 1512, on the death of
his uncle, he finally settled in Frauenburg, in a set of rooms which he
occupied, with short intervals, for the next 31 years. Once fairly in
residence, he took his share in conducting the business of the Chapter:
he acted, for example, more than once as their representative in
various quarrels with the King of Poland and the Teutonic knights; in
1523 he was general administrator of the diocese for a few months after
the death of the bishop; and for two periods, amounting altogether
to six years (1516-1519 and 1520-1521), he lived at the castle of
Allenstein, administering some of the outlying property of the Chapter.
In 1521 he was commissioned to draw up a statement of the grievances
of the Chapter against the Teutonic knights for presentation to the
Prussian Estates, and in the following year wrote a memorandum on the
debased and confused state of the coinage in the district, a paper
which was also laid before the Estates, and was afterwards rewritten
in Latin at the special request of the bishop. He also gave a certain
amount of medical advice to his friends as well as to the poor of
Frauenburg, though he never practised regularly as a physician; but
notwithstanding these various occupations it is probable that a very
large part of his time during the last 30 years of his life was devoted
to astronomy.
73. We are so accustomed to associate the revival of astronomy, as
of other branches of natural science, with increased care in the
collection of observed facts, and to think of Coppernicus as the chief
agent in the revival, that it is worth while here to emphasise the
fact that he was in no sense a great observer. His instruments, which
were mostly of his own construction, were far inferior to those of
Nassir Eddin and of Ulugh Begh (chapter III., §§ 62, 63), and not even
as good as those which he could have procured if he had wished from
the workshops of Nürnberg; his observations were not at all numerous
(only 27, which occur in his book, and a dozen or two besides being
known), and he appears to have made no serious attempt to secure great
accuracy. His determination of the position of one star, which was
extensively used by him as a standard of reference and was therefore of
special importance, was in error to the extent of nearly 40′ (more than
the apparent breadth of the sun or moon), an error which Hipparchus
would have considered very serious. His pupil Rheticus (§ 74) reports
an interesting discussion between his master and himself, in which the
pupil urged the importance of making observations with all imaginable
accuracy; Coppernicus answered that minute accuracy was not to be
looked for at that time, and that a rough agreement between theory and
observation was all that he could hope to attain. Coppernicus moreover
points out in more than one place that the high latitude of Frauenburg
and the thickness of the air were so detrimental to good observation
that, for example, though he had occasionally been able to see the
planet Mercury, he had never been able to observe it properly.
Although he published nothing of importance till towards the end of his
life, his reputation as an astronomer and mathematician appears to have
been established among experts from the date of his leaving Italy, and
to have steadily increased as time went on.
In 1515 he was consulted by a committee appointed by the Lateran
Council to consider the reform of the calendar, which had now fallen
into some confusion (chapter II., § 22), but he declined to give any
advice on the ground that the motions of the sun and moon were as yet
too imperfectly known for a satisfactory reform to be possible. A few
years later (1524) he wrote an open letter, intended for publication,
to one of his Cracow friends, in reply to a tract on precession, in
which, after the manner of the time, he used strong language about the
errors of his opponent.[46]
It was meanwhile gradually becoming known that he held the novel
doctrine that the earth was in motion and the sun and stars at
rest, a doctrine which was sufficiently startling to attract notice
outside astronomical circles. About 1531 he had the distinction of
being ridiculed on the stage at some popular performance in the
neighbourhood; and it is interesting to note (especially in view of the
famous persecution of Galilei at Rome a century later) that Luther in
his _Table Talk_ frankly described Coppernicus as a fool for holding
such opinions, which were obviously contrary to the Bible, and that
Melanchthon, perhaps the most learned of the Reformers, added to a
somewhat similar criticism a broad hint that such opinions should not
be tolerated. Coppernicus appears to have taken no notice of these or
similar attacks, and still continued to publish nothing. No observation
made later than 1529 occurs in his great book, which seems to have been
nearly in its final form by that date; and to about this time belongs
an extremely interesting paper, known as the _Commentariolus_, which
contains a short account of his system of the world, with some of
the evidence for it, but without any calculations. It was apparently
written to be shewn or lent to friends, and was not published; the
manuscript disappeared after the death of the author and was only
rediscovered in 1878. The _Commentariolus_ was probably the basis of a
lecture on the ideas of Coppernicus given in 1533 by one of the Roman
astronomers at the request of Pope Clement VII. Three years later
Cardinal Schomberg wrote to ask Coppernicus for further information as
to his views, the letter showing that the chief features were already
pretty accurately known.
74. Similar requests must have been made by others, but his final
decision to publish his ideas seems to have been due to the arrival at
Frauenburg in 1539 of the enthusiastic young astronomer generally known
as _Rheticus_.[47] Born in 1514, he studied astronomy under Schoner at
Nürnberg, and was appointed in 1536 to one of the chairs of mathematics
created by the influence of Melanchthon at Wittenberg, at that time the
chief Protestant University.
Having heard, probably through the _Commentariolus_, of Coppernicus
and his doctrines, he was so much interested in them that he decided
to visit the great astronomer at Frauenburg. Coppernicus received him
with extreme kindness, and the visit, which was originally intended to
last a few days or weeks, extended over nearly two years. Rheticus set
to work to study Coppernicus’s manuscript, and wrote within a few weeks
of his arrival an extremely interesting and valuable account of it,
known as the First Narrative (_Prima Narratio_), in the form of an open
letter to his old master Schoner, a letter which was printed in the
following spring and was the first easily accessible account of the new
doctrines.[48]
When Rheticus returned to Wittenberg, towards the end of 1541, he took
with him a copy of a purely mathematical section of the great book,
and had it printed as a textbook of the subject (Trigonometry); it had
probably been already settled that he was to superintend the printing
of the complete book itself. Coppernicus, who was now an old man and
would naturally feel that his end was approaching, sent the manuscript
to his friend Giese, Bishop of Kulm, to do what he pleased with.
Giese sent it at once to Rheticus, who made arrangements for having
it printed at Nürnberg. Unfortunately Rheticus was not able to see it
all through the press, and the work had to be entrusted to Osiander, a
Lutheran preacher interested in astronomy. Osiander appears to have
been much alarmed at the thought of the disturbance which the heretical
ideas of Coppernicus would cause, and added a prefatory note of his
own (which he omitted to sign), praising the book in a vulgar way, and
declaring (what was quite contrary to the views of the author) that the
fundamental principles laid down in it were merely abstract hypotheses
convenient for purposes of calculation; he also gave the book the
title _De Revolutionibus Orbium Celestium_ (On the Revolutions of the
Celestial Spheres), the last two words of which were probably his own
addition. The printing was finished in the winter 1542-3, and the
author received a copy of his book on the day of his death (May 24th,
1543), when his memory and mental vigour had already gone.
75. The central idea with which the name of Coppernicus is associated,
and which makes the _De Revolutionibus_ one of the most important books
in all astronomical literature, by the side of which perhaps only the
_Almagest_ and Newton’s _Principia_ (chapter IX., §§ 177 _seqq._) can
be placed, is that the apparent motions of the celestial bodies are to
a great extent not real motions, but are due to the motion of the earth
carrying the observer with it. Coppernicus tells us that he had long
been struck by the unsatisfactory nature of the current explanations of
astronomical observations, and that, while searching in philosophical
writings for some better explanation, he had found a reference of
Cicero to the opinion of Hicetas that the earth turned round on its
axis daily. He found similar views held by other Pythagoreans, while
Philolaus and Aristarchus of Samos had also held that the earth not
only rotates, but moves bodily round the sun or some other centre (cf.
chapter II., § 24). The opinion that the earth is not the sole centre
of motion, but that Venus and Mercury revolve round the sun, he found
to be an old Egyptian belief, supported also by _Martianus Capella_,
who wrote a compendium of science and philosophy in the 5th or 6th
century A.D. A more modern authority, _Nicholas of Cusa_ (1401-1464), a
mystic writer who refers to a possible motion of the earth, was ignored
or not noticed by Coppernicus. None of the writers here named, with
the possible exception of Aristarchus of Samos, to whom Coppernicus
apparently paid little attention, presented the opinions quoted as
more than vague speculations; none of them gave any substantial reasons
for, much less a proof of, their views; and Coppernicus, though he
may have been glad, after the fashion of the age, to have the support
of recognised authorities, had practically to make a fresh start and
elaborate his own evidence for his opinions.
It has sometimes been said that Coppernicus _proved_ what earlier
writers had guessed at or suggested; it would perhaps be truer to say
that he took up certain floating ideas, which were extremely vague
and had never been worked out scientifically, based on them certain
definite fundamental principles, and from these principles developed
mathematically an astronomical system which he shewed to be at least as
capable of explaining the observed celestial motions as any existing
variety of the traditional Ptolemaic system. The Coppernican system,
as it left the hands of the author, was in fact decidedly superior to
its rivals as an explanation of ordinary observations, an advantage
which it owed quite as much to the mathematical skill with which it
was developed as to its first principles; it was in many respects very
much simpler; and it avoided certain fundamental difficulties of the
older system. It was however liable to certain serious objections,
which were only overcome by fresh evidence which was subsequently
brought to light. For the predecessors of Coppernicus there was, apart
from variations of minor importance, but one scientific system which
made any serious attempt to account for known facts; for his immediate
successors there were two, the newer of which would to an impartial
mind appear on the whole the more satisfactory, and the further study
of the two systems, with a view to the discovery of fresh arguments
or fresh observations tending to support the one or the other, was
immediately suggested as an inquiry of first-rate importance.
76. The plan of the _De Revolutionibus_ bears a general resemblance to
that of the _Almagest_. In form at least the book is not primarily an
argument in favour of the motion of the earth, and it is possible to
read much of it without ever noticing the presence of this doctrine.
Coppernicus, like Ptolemy, begins with certain first principles
or postulates, but on account of their novelty takes a little more
trouble than his predecessor (cf. chapter II., § 47) to make them at
once appear probable. With these postulates as a basis he proceeds
to develop, by means of elaborate and rather tedious mathematical
reasoning, aided here and there by references to observations, detailed
schemes of the various celestial motions; and it is by the agreement
of these calculations with observations, far more than by the general
reasoning given at the beginning, that the various postulates are in
effect justified.
His first postulate, that the universe is spherical, is supported by
vague and inconclusive reasons similar to those given by Ptolemy and
others; for the spherical form of the earth he gives several of the
usual valid arguments, one of his proofs for its curvature from east to
west being the fact that eclipses visible at one place are not visible
at another. A third postulate, that the motions of the celestial bodies
are uniform circular motions or are compounded of such motions, is, as
might be expected, supported only by reasons of the most unsatisfactory
character. He argues, for example, that any want of uniformity in motion
“must arise either from irregularity in the moving power, whether this
be within the body or foreign to it, or from some inequality of the
body in revolution.... Both of which things the intellect shrinks from
with horror, it being unworthy to hold such a view about bodies which
are constituted in the most perfect order.”
77. The discussion of the possibility that the earth may move, and may
even have more than one motion, then follows, and is more satisfactory
though by no means conclusive. Coppernicus has a firm grasp of the
principle, which Aristotle had also enunciated, sometimes known as that
of relative motion, which he states somewhat as follows:—
“For all change in position which is seen is due to a motion
either of the observer or of the thing looked at, or to changes in
the position of both, provided that these are different. For when
things are moved equally relatively to the same things, no motion is
perceived, as between the object seen and the observer.”[49]
Coppernicus gives no proof of this principle, regarding it probably
as sufficiently obvious, when once stated, to the mathematicians and
astronomers for whom he was writing. It is, however, so fundamental
that it may be worth while to discuss it a little more fully.
[Illustration: FIG. 37.—Relative motion.]
Let, for example, the observer be at A and an object at B, then whether
the object move from B to B′, the observer remaining at rest, or the
observer move an _equal_ distance in the _opposite_ direction, from A
to A′, the object remaining at rest, the effect is to the eye exactly
the same, since in either case the distance between the observer and
object and the direction in which the object is seen, represented in
the first case by A B′ and in the second by A′ B, are the same.
Thus if in the course of a year _either_ the sun passes successively
through the positions A, B, C, D (fig. 38), the earth remaining at rest
at E, _or_ if the sun is at rest and the earth passes successively
through the positions _a_, _b_, _c_, _d_, at the corresponding times,
the sun remaining at rest at S, exactly the same effect is produced
on the eye, provided that the lines _a_ S, _b_ S, _c_ S, _d_ S are,
as in the figure, equal in length and parallel in direction to E
A, E B, E C, E D respectively. The same being true of intermediate
points, exactly the same apparent effect is produced whether the sun
describe the circle A B C D, or the earth describe at the same rate
the equal circle _a b c d_. It will be noticed further that, although
the corresponding motions in the two cases are at the same times in
_opposite_ directions (as at A and _a_), yet each circle as a whole
is described, as indicated by the arrowheads, in the _same_ direction
(contrary to that of the motion of the hands of a clock, in the figures
given). It follows in the same sort of way that an apparent motion (as
of a planet) may be explained as due partially to the motion of the
object, partially to that of the observer.
[Illustration: FIG. 38.—The relative motion of the sun and moon.]
Coppernicus gives the familiar illustration of the passenger in a boat
who sees the land apparently moving away from him, by quoting and
explaining Virgil’s line:—
“Provehimur portu, terræque urbesque recedunt.”
[Illustration: FIG. 39.—The daily rotation of the earth.]
78. The application of the same ideas to an apparent rotation round
the observer, as in the case of the apparent daily motion of the
celestial sphere, is a little more difficult. It must be remembered
that the eye has no means of judging the direction of an object taken
by itself; it can only judge the difference between the direction of
the object and some other direction, whether that of another object or
a direction fixed in some way by the body of the observer. Thus when
after looking at a star twice at an interval of time we decide that it
has moved, this means that its direction has changed relatively to,
say, some tree or house which we had noticed nearly in its direction,
or that its direction has changed relatively to the direction in which
we are directing our eyes or holding our bodies. Such a change can
evidently be interpreted as a change of direction, either of the star
or of the line from the eye to the tree which we used as a line of
reference. To apply this to the case of the celestial sphere, let us
suppose that S represents a star on the celestial sphere, which (for
simplicity) is overhead to an observer on the earth at A, this being
determined by comparison with a line A B drawn upright on the earth.
Next, earth and celestial sphere being supposed to have a common centre
at O, let us suppose _firstly_ that the celestial sphere turns round
(in the direction of the hands of a clock) till S comes to S′, and
that the observer now sees the star on his horizon or in a direction
at right angles to the original direction A B, the angle turned
through by the celestial sphere being S O S′; and _secondly_ that, the
celestial sphere being unchanged, the earth turns round in the opposite
direction, till A B comes to A′ B′, and the star is again seen by the
observer on his horizon. Whichever of these motions has taken place,
the observer sees exactly the same apparent motion in the sky; and the
figure shews at once that the angle S O S′ through which the celestial
sphere was supposed to turn in the first case is equal to the angle A O
A′ through which the earth turns in the second case, but that the two
rotations are in opposite directions. A similar explanation evidently
applies to more complicated cases.
Hence the apparent daily rotation of the celestial sphere about an axis
through the poles would be produced equally well, either by an actual
rotation of this character, or by a rotation of the earth about an
axis also passing through the poles, and at the same rate, but in the
opposite direction, _i.e._ from west to east. This is the first motion
which Coppernicus assigns to the earth.
79. The apparent annual motion of the sun, in accordance with which
it appears to revolve round the earth in a path which is nearly a
circle, can be equally well explained by supposing the sun to be at
rest, and the earth to describe an exactly equal path round the sun,
the direction of the revolution being the same. This is virtually the
second motion which Coppernicus gives to the earth, though, on account
of a peculiarity in his geometrical method, he resolves this motion
into two others, and combines with one of these a further small motion
which is required for precession.[50]
80. Coppernicus’s conception then is that the earth revolves round the
sun in the plane of the ecliptic, while rotating daily on an axis which
continually points to the poles of the celestial sphere, and therefore
retains (save for precession) a fixed direction in space.
It should be noticed that the two motions thus assigned to the earth
are perfectly distinct; each requires its own proof, and explains a
different set of appearances. It was quite possible, with perfect
consistency, to believe in one motion without believing in the other,
as in fact a very few of the 16th-century astronomers did (chapter V.,
§ 105).
In giving his reasons for believing in the motion of the earth
Coppernicus discusses the chief objections which had been urged by
Ptolemy. To the objection that if the earth had a rapid motion of
rotation about its axis, the earth would be in danger of flying to
pieces, and the air, as well as loose objects on the surface, would be
left behind, he replies that if such a motion were dangerous to the
solid earth, it must be much more so to the celestial sphere, which,
on account of its vastly greater size, would have to move enormously
faster than the earth to complete its daily rotation; he enters also
into an obscure discussion of difference between a “natural” and an
“artificial” motion, of which the former might be expected not to
disturb anything on the earth.
Coppernicus shews that the earth is very small compared to the sphere
of the stars, because wherever the observer is on the earth the horizon
appears to divide the celestial sphere into two equal parts and the
observer appears always to be at the centre of the sphere, so that any
distance through which the observer moves on the earth is imperceptible
as compared with the distance of the stars.
81. He goes on to argue that the chief irregularity in the motion
of the planets, in virtue of which they move backwards at intervals
(chapter I., § 14, and chapter II., § 51), can readily be explained
in general by the motion of the earth and by a motion of each planet
round the sun, in its own time and at its own distance. From the fact
that Venus and Mercury were never seen very far from the sun, it could
be inferred that their paths were nearer to the sun than that of the
earth. Mercury being the nearer to the sun of the two, because never
seen so far from it in the sky as Venus. The other three planets,
being seen at times in a direction opposite to that of the sun, must
necessarily evolve round the sun in orbits larger than that of the
earth, a view confirmed by the fact that they were brightest when
opposite the sun (in which positions they would be nearest to us).
The order of their respective distances from the sun could be at once
inferred from the disturbing effects produced on their apparent motions
by the motion of the earth; Saturn being least affected must on the
whole be farthest from the earth, Jupiter next, and Mars next. The
earth thus became one of six planets revolving round the sun, the
order of distance—Mercury, Venus, Earth, Mars, Jupiter, Saturn—being
also in accordance with the rates of motion round the sun, Mercury
performing its revolution most rapidly (in about 88 days[51]), Saturn
most slowly (in about 30 years). On the Coppernican system the moon
alone still revolved round the earth, being the only celestial body the
status of which was substantially unchanged; and thus Coppernicus was
able to give the accompanying diagram of the solar system (fig. 40),
representing his view of its general arrangement (though not of the
right proportions of the different parts) and of the various motions.
[Illustration: FIG. 40.—The solar system according to Coppernicus. From
the _De Revolutionibus_.]
82. The effect of the motion of the earth round the sun on the length
of the day and other seasonal effects is discussed in some detail, and
illustrated by diagrams which are here reproduced.[52]
[Illustration: FIG. 41.—Coppernican explanation of the seasons. From
the _De Revolutionibus_.]
[Illustration: FIG. 42.—Coppernican explanation of the seasons. From
the _De Revolutionibus_.]
In fig. 41 A, B, C, D represent the centre of the earth in four
positions, occupied by it about December 23rd, March 21st, June 22nd,
and September 22nd respectively (_i.e._ at the beginnings of the four
seasons, according to astronomical reckoning); the circle F G H I in
each of its positions represents the equator of the earth, _i.e._ a
great circle on the earth the plane of which is perpendicular to the
axis of the earth and is consequently always parallel to the celestial
equator. This circle is not in the plane of the ecliptic, but tilted
up at an angle of 23-1∕2°, so that F must always be supposed _below_
and H _above_ the plane of the paper (which represents the ecliptic);
the equator cuts the ecliptic along G I. The diagram (in accordance
with the common custom in astronomical diagrams) represents the various
circles as seen from the north side of the equator and ecliptic. When
the earth is at A, the north pole (as is shewn more clearly in fig.
42, in which P, P′ denote the north pole and south pole respectively)
is turned away from the sun, E, which is on the lower or south side of
the plane of the equator, and consequently inhabitants of the northern
hemisphere see the sun for less than half the day, while those on
the southern hemisphere see the sun for more than half the day, and
those beyond the line K L (in fig. 42) see the sun during the whole
day. Three months later, when the earth’s centre is at B (fig. 41),
the sun lies in the plane of the equator, the poles of the earth are
turned neither towards nor away from the sun, but aside, and all over
the earth daylight lasts for 12 hours and night for an equal time.
Three months later still, when the earth’s centre is at C, the sun is
above the plane of the equator, and the inhabitants of the northern
hemisphere see the sun for more than half the day, those on the
southern hemisphere for less than half, while those in parts of the
earth farther north than the line M N (in fig. 42) see the sun for the
whole 24 hours. Finally, when, at the autumn equinox, the earth has
reached D (fig. 41), the sun is again in the plane of the equator, and
the day is everywhere equal to the night.
83. Coppernicus devotes the first eleven chapters of the first book
to this preliminary sketch of his system; the remainder of this book
he fills with some mathematical propositions and tables, which, as
previously mentioned (§ 74), had already been separately printed by
Rheticus. The second book contains chiefly a number of the usual
results relating to the celestial sphere and its apparent daily motion,
treated much as by earlier writers, but with greater mathematical
skill. Incidentally Coppernicus gives his measurement of the obliquity
of the ecliptic, and infers from a comparison with earlier observations
that the obliquity had decreased, which was in fact the case, though
to a much less extent than his imperfect observations indicated. The
book ends with a catalogue of stars, which is Ptolemy’s catalogue,
occasionally corrected by fresh observations, and rearranged so as to
avoid the effects of precession.[53] When, as frequently happened, the
Greek and Latin versions of the _Almagest_ gave, owing to copyists’
or printers’ errors, different results, Coppernicus appears to have
followed sometimes the Latin and sometimes the Greek version, without
in general attempting to ascertain by fresh observations which was
right.
84. The third book begins with an elaborate discussion of the
precession of the equinoxes (chapter II., § 42). From a comparison
of results obtained by Timocharis, by later Greek astronomers, and
by Albategnius, Coppernicus infers that the amount of precession has
varied, but that its average value is 50″·2 annually (almost exactly
the true value), and accepts accordingly Tabit ben Korra’s unhappy
suggestion of the trepidation (chapter III., § 58). An examination of
the data used by Coppernicus shews that the erroneous or fraudulent
observations of Ptolemy (chapter II., § 50) are chiefly responsible for
the perpetuation of this mistake.
Of much more interest than the detailed discussion of trepidation and
of geometrical schemes for representing it is the interpretation of
precession as the result of a motion of the earth’s axis. Precession
was originally recognised by Hipparchus as a motion of the celestial
equator, in which its inclination to the ecliptic was sensibly
unchanged. Now the ideas of Coppernicus make the celestial equator
dependent on the equator of the earth, and hence on its axis; it
is in fact a great circle of the celestial sphere which is always
perpendicular to the axis about which the earth rotates daily. Hence
precession, on the theory of Coppernicus, arises from a slow motion of
the axis of the earth, which moves so as always to remain inclined at
the same angle to the ecliptic, and to return to its original position
after a period of about 26,000 years (since a motion of 50″·2 annually
is equivalent to 360° or a complete circuit in that period); in other
words, the earth’s axis has a slow conical motion, the central line (or
axis) of the cone being at right angles to the plane of the ecliptic.
85. Precession being dealt with, the greater part of the remainder of
the third book is devoted to a discussion in detail of the apparent
annual motion of the sun round the earth, corresponding to the real
annual motion of the earth round the sun. The geometrical theory of
the _Almagest_ was capable of being immediately applied to the new
system, and Coppernicus, like Ptolemy, uses an eccentric. He makes the
calculations afresh, arrives at a smaller and more accurate value of
the eccentricity (about 1∕31 instead of 1∕24), fixes the position of
the apogee and perigee (chapter II., § 39), or rather of the equivalent
=aphelion= and =perihelion= (_i.e._ the points in the earth’s orbit
where it is respectively farthest from and nearest to the sun), and
thus verifies Albategnius’s discovery (chapter III., § 59) of the
motion of the line of apses. The theory of the earth’s motion is worked
out in some detail, and tables are given whereby the apparent place of
the sun at any time can be easily computed.
The fourth book deals with the theory of the moon. As has been already
noticed, the moon was the only celestial body the position of which
in the universe was substantially unchanged by Coppernicus, and it
might hence have been expected that little alteration would have
been required in the traditional theory. Actually, however, there
is scarcely any part of the subject in which Coppernicus did more to
diminish the discrepancies between theory and observation. He rejects
Ptolemy’s equant (chapter II., § 51), partly on the ground that it
produces an irregular motion unsuitable for the heavenly bodies, partly
on the more substantial ground that, as already pointed out (chapter
II., § 48), Ptolemy’s theory makes the apparent size of the moon at
times twice as great as at others. By an arrangement of epicycles
Coppernicus succeeded in representing the chief irregularities in the
moon’s motion, including evection, but without Ptolemy’s prosneusis
(chapter II., § 48) or Abul Wafa’s inequality (chapter III., § 60),
while he made the changes in the moon’s distance, and consequently in
its apparent size, not very much greater than those which actually
take place, the difference being imperceptible by the rough methods of
observation which he used.[54]
In discussing the distances and sizes of the sun and moon Coppernicus
follows Ptolemy closely (chapter II., § 49; cf. also fig. 20); he
arrives at substantially the same estimate of the distance of the moon,
but makes the sun’s distance 1,500 times the earth’s radius, thus
improving to some extent on the traditional estimate, which was based
on Ptolemy’s. He also develops in some detail the effect of parallax
on the apparent place of the moon, and the variations in the apparent
size, owing to the variations in distance: and the book ends with a
discussion of eclipses.
86. The last two books (V. and VI.) deal at length with the motion of
the planets.
In the cases of Mercury and Venus, Ptolemy’s explanation of the
motion could with little difficulty be rearranged so as to fit the
ideas of Coppernicus. We have seen (chapter II., § 51) that, minor
irregularities being ignored, the motion of either of these planets
could be represented by means of an epicycle moving on a deferent, the
centre of the epicycle being always in the direction of the sun, the
ratio of the sizes of the epicycle and deferent being fixed, but the
actual dimensions being practically arbitrary. Ptolemy preferred on the
whole to regard the epicycles of both these planets as lying between
the earth and the sun. The idea of making the sun a centre of motion
having once been accepted, it was an obvious simplification to make
the centre of the epicycle not merely lie in the direction of the sun,
but actually be the sun. In fact, if the planet in question revolved
round the sun at the proper distance and at the proper rate, the same
appearances would be produced as by Ptolemy’s epicycle and deferent,
the path of the planet round the sun replacing the epicycle, and the
apparent path of the sun round the earth (or the path of the earth
round the sun) replacing the deferent.
[Illustration: FIG. 43.—The orbits of Venus and of the earth.]
[Illustration: FIG. 44.—The synodic and sidereal periods of Venus.]
In discussing the time of revolution of a planet a distinction has to
be made, as in the case of the moon (chapter II., § 40), between the
synodic and sidereal periods of revolution. Venus, for example, is
seen as an evening star at its greatest angular distance from the sun
(as at V in fig. 43) at intervals of about 584 days. This is therefore
the time which Venus takes to return to the same position relatively
to the sun, as seen from the earth, or relatively to the earth, as
seen from the sun; this time is called the =synodic period=. But as
during this time the line E S has changed its direction, Venus is no
longer in the same position relatively to the stars, as seen either
from the sun or from the earth. If at first Venus and the earth are at
V_{1}, E_{1}; respectively, after 584 days (or about a year and seven
months) the earth will have performed rather more than a revolution and
a half round the sun and will be at E_{2}; Venus being again at the
greatest distance from the sun will therefore be at V_{2}, but will
evidently be seen in quite a different part of the sky, and will not
have performed an exact revolution round the sun. It is important to
know how long the line S V_{1} takes to return to the same position,
_i.e._ how long Venus takes to return to the same position with respect
to the stars, as seen from the sun, an interval of time known as
the =sidereal period=. This can evidently be calculated by a simple
rule-of-three sum from the data given. For Venus has in 584 days gained
a complete revolution on the earth, or has gone as far as the earth
would have gone in 584 + 365 or 949 days (fractions of days being
omitted for simplicity); hence Venus goes in 584 × 365∕949 days as far
as the earth in 365 days, _i.e._ Venus completes a revolution in 584 ×
365∕949 or 225 days. This is therefore the sidereal period of Venus.
The process used by Coppernicus was different, as he saw the advantage
of using a long period of time, so as to diminish the error due to
minor irregularities, and he therefore obtained two observations of
Venus at a considerable interval of time, in which Venus occupied very
nearly the same position both with respect to the sun and to the stars,
so that the interval of time contained very nearly an exact number of
sidereal periods as well as of synodic periods. By dividing therefore
the observed interval of time by the number of sidereal periods (which
being a whole number could readily be estimated), the sidereal period
was easily obtained. A similar process shewed that the synodic period
of Mercury was about 116 days, and the sidereal period about 88 days.
The comparative sizes of the orbits of Venus and Mercury as compared
with that of the earth could easily be ascertained from observations of
the position of either planet when most distant from the sun. Venus,
for example, appears at its greatest distance from the sun when at a
point V_{1} (fig. 44) such that V_{1} E_{1} touches the circle in which
Venus moves, and the angle E_{1} V_{1} S is then (by a known property
of a circle) a right angle. The angle S E_{1} V_{1} being observed,
the shape of the triangle S E_{1} V_{1} is known, and the ratio of
its sides can be readily calculated. Thus Coppernicus found that the
average distance of Venus from the sun was about 72 and that of Mercury
about 36, the distance of the earth from the sun being taken to be 100;
the corresponding modern figures are 72·3 and 38·7.
[Illustration: FIG. 45.—The epicycle of Jupiter.]
87. In the case of the superior planets. Mars, Jupiter, and Saturn,
it was much more difficult to recognise that their motions could be
explained by supposing them to revolve round the sun, since the centre
of the epicycle did not always lie in the direction of the sun, but
might be anywhere in the ecliptic. One peculiarity, however, in the
motion of any of the superior planets might easily have suggested their
motion round the sun, and was either completely overlooked by Ptolemy
or not recognised by him as important. It is possible that it was one
of the clues which led Coppernicus to his system. This peculiarity
is that the radius of the epicycle of the planet, _j_ J, is always
parallel to the line E S joining the earth and sun, and consequently
performs a complete revolution in a year. This connection between the
motion of the planet and that of the sun received no explanation from
Ptolemy’s theory. Now if we draw E J′ parallel to _j_ J and equal to
it in length, it is easily seen[55] that the line J′ J is equal and
parallel to E _j_, that consequently J describes a circle round J′
just as _j_ round E. Hence the motion of the planet can equally well
be represented by supposing it to move in an epicycle (represented by
the large dotted circle in the figure) of which J′ is the centre and
J′ J the radius, while the centre of the epicycle, remaining always
in the direction of the sun, describes a deferent (represented by the
small circle round E) of which the earth is the centre. By this method
of representation the motion of the superior planet is exactly like
that of an inferior planet, except that its epicycle is larger than
its deferent; the same reasoning as before shows that the motion can
be represented simply by supposing the centre J′ of the epicycle to be
actually the sun. Ptolemy’s epicycle and deferent are therefore capable
of being replaced, without affecting the position of the planet in the
sky, by a motion of the planet in a circle round the sun, while the
sun moves round the earth, or, more simply, the earth round the sun.
[Illustration: FIG. 46.—The relative sizes of the orbits of the earth
and of a superior planet.]
The synodic period of a superior planet could best be determined
by observing when the planet was in opposition, _i.e._ when it was
(nearly) opposite the sun, or, more accurately (since a planet does
not move exactly in the ecliptic), when the longitudes of the planet
and sun differed by 180° (or two right angles, chapter II., § 43).
The sidereal period could then be deduced nearly as in the case of
an inferior planet, with this difference, that the superior planet
moves more slowly than the earth, and therefore _loses_ one complete
revolution in each synodic period; or the sidereal period might be
found as before by observing when oppositions occurred nearly in
the same part of the sky.[56] Coppernicus thus obtained very fairly
accurate values for the synodic and sidereal periods, _viz._ 780 days
and 687 days respectively for Mars, 399 days and about 12 years for
Jupiter, 378 days and 30 years for Saturn (cf. fig. 40).
The calculation of the distance of a superior planet from the sun is a
good deal more complicated than that of Venus or Mercury. If we ignore
various details, the process followed by Coppernicus is to compute the
position of the planet as seen from the sun, and then to notice when
this position differs most from its position as seen from the earth,
_i.e._ when the earth and sun are farthest apart as seen from the
planet. This is clearly when (fig. 46) the line joining the planet (P)
to the earth (E) touches the circle described by the earth, so that the
angle S P E is then as great as possible. The angle P E S is a right
angle, and the angle S P E is the difference between the observed place
of the planet and its computed place as seen from the sun; these two
angles being thus known, the shape of the triangle S P E is known,
and therefore also the ratio of its sides. In this way Coppernicus
found the average distances of Mars, Jupiter, and Saturn from the sun
to be respectively about 1-1∕2, 5, and 9 times that of the earth; the
corresponding modern figures are 1·5, 5·2, 9·5.
88. The explanation of the stationary points of the planets (chapter
I., § 14) is much simplified by the ideas of Coppernicus. If we take
first an inferior planet, say Mercury (fig. 47), then when it lies
between the earth and sun, as at M (or as on Sept. 5 in fig. 7),
both the earth and Mercury are moving in the same direction, but a
comparison of the sizes of the paths of Mercury and the earth, and of
their respective times of performing complete circuits, shews that
Mercury is moving faster than the earth. Consequently to the observer
at E, Mercury appears to be moving from left to right (in the figure),
or from east to west; but this is contrary to the general direction
of motion of the planets, _i.e._ Mercury appears to be retrograding.
On the other hand, when Mercury appears at the greatest distance from
the sun, as at M_{1} and M_{2}, its own motion is directly towards or
away from the earth, and is therefore imperceptible; but the earth is
moving towards the observer’s right, and therefore Mercury appears to
be moving towards the left, or from west to east. Hence between M_{1}
and M its motion has changed from direct to retrograde, and therefore
at some intermediate point, say _m_{1}_, (about Aug, 23 in fig. 7),
Mercury appears for the moment to be stationary, and similarly it
appears to be stationary again when at some point _m_{2}_ between M and
M_{2} (about Sept. 13 in fig. 7).
[Illustration: FIG. 47.—The stationary points of Mercury.]
In the case of a superior planet, say Jupiter, the argument is nearly
the same. When in opposition at J (as on Mar. 26 in fig. 6), Jupiter
moves more slowly than the earth, and in the same direction, and
therefore appears to be moving in the opposite direction to the earth,
_i.e._ as seen from E (fig. 48), from left to right, or from east to
west, that is in the retrograde direction. But when Jupiter is in
either of the positions J_{1} or J (in which the earth appears to the
observer on Jupiter to be at its greatest distance from the sun), the
motion of the earth itself being directly to or from Jupiter produces
no effect on the apparent motion of Jupiter (since any displacement
directly to or from the observer makes no difference in the object’s
place on the celestial sphere); but Jupiter itself is actually moving
towards the left, and therefore the motion of Jupiter appears to be
also from right to left, or from west to east. Hence, as before,
between J_{1} and J and between J and J_{2} there must be points
_j_{1}_, _j_{2}_ (Jan. 24 and May 27, in fig. 6) at which Jupiter
appears for the moment to be stationary.
[Illustration: FIG. 48.—The stationary points of Jupiter.]
The actual discussion of the stationary points given by Coppernicus is
a good deal more elaborate and more technical than the outline given
here, as he not only shews that the stationary points must exist, but
shews how to calculate their exact positions.
89. So far the theory of the planets has only been sketched very
roughly, in order to bring into prominence the essential differences
between the Coppernican and the Ptolemaic explanations of their
motions, and no account has been taken of the minor irregularities for
which Ptolemy devised his system of equants, eccentrics, etc., nor of
the motion in latitude, _i.e._ to and from the ecliptic. Coppernicus,
as already mentioned, rejected the equant, as being productive of
an irregularity “unworthy” of the celestial bodies, and constructed
for each planet a fairly complicated system of epicycles. For the
motion in latitude discussed in Book VI. he supposed the orbit of each
planet round the sun to be inclined to the ecliptic at a small angle,
different for each planet, but found it necessary, in order that his
theory should agree with observation, to introduce the wholly imaginary
complication of a regular increase and decrease in the inclinations of
the orbits of the planets to the ecliptic.
The actual details of the epicycles employed are of no great interest
now, but it may be worth while to notice that for the motions of the
moon, earth, and five other planets Coppernicus required altogether
34 circles, _viz._ four for the moon, three for the earth, seven for
Mercury (the motion of which is peculiarly irregular), and five for
each of the other planets; this number being a good deal less than that
required in most versions of Ptolemy’s system: Fracastor (chapter III.,
§ 69), for example, writing in 1538, required 79 spheres, of which six
were required for the fixed stars.
90. The planetary theory of Coppernicus necessarily suffered from one
of the essential defects of the system of epicycles. It is, in fact,
always possible to choose a system of epicycles in such a way as to
make _either_ the direction of any body _or_ its distance vary in any
required manner, but not to satisfy both requirements at once. In the
case of the motion of the moon round the earth, or of the earth round
the sun, cases in which variations in distance could not readily be
observed, epicycles might therefore be expected to give a satisfactory
result, at any rate until methods of observation were sufficiently
improved to measure with some accuracy the apparent sizes of the sun
and moon, and so check the variations in their distances. But any
variation in the distance of the earth from the sun would affect not
merely the distance, but also the direction in which a planet would be
seen; in the figure, for example, when the planet is at P and the sun
at S, the apparent position of the planet, as seen from the earth, will
be different according as the earth is at E or E′. Hence the epicycles
and eccentrics of Coppernicus, which had to be adjusted in such a
way that they necessarily involved incorrect values of the distances
between the sun and earth, gave rise to corresponding errors in the
observed places of the planets. The observations which Coppernicus
used were hardly extensive or accurate enough to show this discrepancy
clearly; but a crucial test was thus virtually suggested by means
of which, when further observations of the planets had been made, a
decision could be taken between an epicyclic representation of the
motion of the planets and some other geometrical scheme.
[Illustration: FIG. 49.—The alteration in a planet’s apparent position
due to an alteration in the earth’s distance from the sun.]
91. The merits of Coppernicus are so great, and the part which he
played in the overthrow of the Ptolemaic system is so conspicuous,
that we are sometimes liable to forget that, so far from rejecting the
epicycles and eccentrics of the Greeks, he used no other geometrical
devices, and was even a more orthodox “epicyclist” than Ptolemy
himself, as he rejected the equants of the latter.[57] Milton’s famous
description (_Par. Lost_, VIII. 82-5) of
“The Sphere
With Centric and Eccentric scribbled o’er,
Cycle and Epicycle, Orb in Orb,”
applies therefore just as well to the astronomy of Coppernicus as to
that of his predecessors; and it was Kepler (chapter VII.), writing
more than half a century later, not Coppernicus, to whom the rejection
of the epicycle and eccentric is due.
92. One point which was of importance in later controversies deserves
special mention here. The basis of the Coppernican system was that a
motion of the earth carrying the observer with it produced an apparent
motion of other bodies. The apparent motions of the sun and planets
were thus shewn to be in great part explicable as the result of the
motion of the earth round the sun. Similar reasoning ought apparently
to lead to the conclusion that the fixed stars would also appear to
have an annual motion. There would, in fact, be a displacement of
the apparent position of a star due to the alteration of the earth’s
position in its orbit, closely resembling the alteration in the
apparent position of the moon due to the alteration of the observer’s
position on the earth which had long been studied under the name of
parallax (chapter II., § 43). As such a displacement had never been
observed, Coppernicus explained the apparent contradiction by supposing
the fixed stars so far off that any motion due to this cause was too
small to be noticed. If, for example, the earth moves in six months
from E to E′, the change in direction of a star at S′ is the angle E′
S′ E, which is less than that of a nearer star at S; and by supposing
the star S′ sufficiently remote, the angle E′ S′ E can be made as small
as may be required. For instance, if the distance of the star were 300
times the distance E E′, _i.e._ 600 times as far from the earth as the
sun is, the angle E S′ E′ would be less than 12′, a quantity which the
instruments of the time were barely capable of detecting.[58] But more
accurate observations of the fixed stars might be expected to throw
further light on this problem.
[Illustration: FIG. 50.—Stellar parallax.]