THE RECEPTION OF THE COPPERNICAN THEORY AND THE PROGRESS OF OBSERVATION.
“Preposterous wits that cannot row at ease
On the smooth channel of our common seas;
And such are those, in my conceit at least,
Those clerks that think—think how absurd a jest!
That neither heavens nor stars do turn at all
Nor dance about this great round Earthly Ball,
But the Earth itself, this massy globe of ours,
Turns round about once every twice twelve hours!”
DU BARTAS (Sylvester’s translation).
93. The publication of the _De Revolutionibus_ appears to have been
received much more quietly than might have been expected from the
startling nature of its contents. The book, in fact, was so written
as to be unintelligible except to mathematicians of considerable
knowledge and ability, and could not have been read at all generally.
Moreover the preface, inserted by Osiander but generally supposed to
be by the author himself, must have done a good deal to disarm the
hostile criticism due to prejudice and custom, by representing the
fundamental principles of Coppernicus as mere geometrical abstractions,
convenient for calculating the celestial motions. Although, as we
have seen (chapter IV., § 73), the contradiction between the opinions
of Coppernicus and the common interpretation of various passages in
the Bible was promptly noticed by Luther, Melanchthon, and others, no
objection was raised either by the Pope to whom the book was dedicated,
or by his immediate successors.
The enthusiastic advocacy of the Coppernican views by Rheticus has
already been referred to. The only other astronomer of note who at
once accepted the new views was his friend and colleague _Erasmus
Reinhold_ (born at Saalfeld in 1511), who occupied the chief chair
of mathematics and astronomy at Wittenberg from 1536 to 1553, and it
thus happened, curiously enough, that the doctrines so emphatically
condemned by two of the great Protestant leaders were championed
principally in what was generally regarded as the very centre of
Protestant thought.
94. Rheticus, after the publication of the _Narratio Prima_ and of an
Ephemeris or Almanack based on Coppernican principles (1550), occupied
himself principally with the calculation of a very extensive set of
mathematical tables, which he only succeeded in finishing just before
his death in 1576.
Reinhold rendered to astronomy the extremely important service of
calculating, on the basis of the _De Revolutionibus_, tables of the
motions of the celestial bodies, which were published in 1551 at the
expense of Duke Albert of Prussia and hence called _Tabulæ Prutenicæ_,
or _Prussian Tables_. Reinhold revised most of the calculations made
by Coppernicus, whose arithmetical work was occasionally at fault; but
the chief object of the tables was the development in great detail of
the work in the _De Revolutionibus_, in such a form that the places of
the chief celestial bodies at any required time could be ascertained
with ease. The author claimed for his tables that from them the places
of all the heavenly bodies could be computed for the past 3,000 years,
and would agree with all observations recorded during that period. The
tables were indeed found to be on the whole decidedly superior to their
predecessors the _Alfonsine Tables_ (chapter III., § 66), and gradually
came more and more into favour, until superseded three-quarters of a
century later by the _Rudolphine Tables_ of Kepler (chapter VII., §
148). This superiority of the new tables was only indirectly connected
with the difference in the principles on which the two sets of tables
were based, and was largely due to the facts that Reinhold was a much
better computer than the assistants of Alfonso, and that Coppernicus,
if not a better mathematician than Ptolemy, at any rate had better
mathematical tools at command. Nevertheless the tables naturally, had
great weight in inducing the astronomical world gradually to recognise
the merits of the Coppernican system, at any rate as a basis for
calculating the places of the celestial bodies.
Reinhold was unfortunately cut off by the plague in 1553, and with
him disappeared a commentary on the _De Revolutionibus_ which he had
prepared but not published.
95. Very soon afterwards we find the first signs that the Coppernican
system had spread into England. In 1556 _John Field_ published an
almanack for the following year avowedly based on Coppernicus and
Reinhold, and a passage in the _Whetstone of Witte_ (1557) by _Robert
Recorde_ (1510-1558), our first writer on algebra, shews that the
author regarded the doctrines of Coppernicus with favour, even if
he did not believe in them entirely. A few years later _Thomas
Digges_ (?-1595), in his _Alae sive Scalae Mathematicae_ (1573), an
astronomical treatise of no great importance, gave warm praise to
Coppernicus and his ideas.
96. For nearly half a century after the death of Reinhold no important
contributions were made to the Coppernican controversy. Reinhold’s
tables were doubtless slowly doing their work in familiarising men’s
minds with the new ideas, but certain definite additions to knowledge
had to be made before the evidence for them could be regarded as really
conclusive.
The serious mechanical difficulties connected with the assumption
of a rapid motion of the earth which is quite imperceptible to its
inhabitants could only be met by further progress in mechanics, and
specially in knowledge of the laws according to which the motion of
bodies is produced, kept up, changed, or destroyed; in this direction
no considerable progress was made before the time of Galilei, whose
work falls chiefly into the early 17th century (cf. chapter VI., §§
116, 130, 133).
The objection to the Coppernican scheme that the stars shewed no such
apparent annual motions as the motion of the earth should produce
(chapter IV., § 92) would also be either answered or strengthened
according as improved methods of observation did or did not reveal the
required motion.
Moreover the _Prussian Tables_, although more accurate than
the _Alfonsine_, hardly claimed, and certainly did not possess,
minute accuracy. Coppernicus had once told Rheticus that he would
be extravagantly pleased if he could make his theory agree with
observation to within 10′; but as a matter of fact discrepancies
of a much more serious character were noticed from time to time.
The comparatively small number of observations available and their
roughness made it extremely difficult, either to find the most
satisfactory numerical data necessary for the detailed development of
any theory, or to test the theory properly by comparison of calculated
with observed places of the celestial bodies. Accordingly it became
evident to more than one astronomer that one of the most pressing
needs of the science was that observations should be taken on as large
a scale as possible and with the utmost attainable accuracy. To meet
this need two schools of observational astronomy, of very unequal
excellence, developed during the latter half of the 16th century, and
provided a mass of material for the use of the astronomers of the
next generation. Fortunately too the same period was marked by rapid
progress in algebra and allied branches of mathematics. Of the three
great inventions which have so enormously diminished the labour of
numerical calculations, one, the so-called Arabic notation (chapter
III., § 64), was already familiar, the other two (decimal fractions
and logarithms) were suggested in the 16th century and were in working
order early in the 17th century.
97. The first important set of observations taken after the death of
Regiomontanus and Walther (chapter III., § 68) were due to the energy
of the Landgrave _William IV._ of Hesse (1532-1592). He was remarkable
as a boy for his love of study, and is reported to have had his
interest in astronomy created or stimulated when he was little more
than 20 by a copy of Apian’s beautiful _Astronomicum Caesareum_, the
cardboard models in which he caused to be imitated and developed in
metal-work. He went on with the subject seriously, and in 1561 had an
observatory built at Cassel, which was remarkable as being the first
which had a revolving roof, a device now almost universal. In this he
made extensive observations (chiefly of fixed stars) during the next
six years. The death of his father then compelled him to devote most
of his energy to the duties of government, and his astronomical ardour
abated. A few years later, however (1575), as the result of a short
visit from the talented and enthusiastic young Danish astronomer Tycho
Brahe (§ 99), he renewed his astronomical work, and secured shortly
afterwards the services of two extremely able assistants, _Christian
Rothmann_ (in 1577) and _Joost Bürgi_ (in 1579). Rothmann, of whose
life extremely little is known, appears to have been a mathematician
and theoretical astronomer of considerable ability, and was the author
of several improvements in methods of dealing with various astronomical
problems. He was at first a Coppernican, but shewed his independence
by calling attention to the needless complication introduced by
Coppernicus in resolving the motion of the earth into _three_ motions
when two sufficed (chapter IV., § 79). His faith in the system was,
however, subsequently shaken by the errors which observation revealed
in the _Prussian Tables_. Bürgi (1552-1632) was originally engaged by
the Landgrave as a clockmaker, but his remarkable mechanical talents
were soon turned to astronomical account, and it then appeared that he
also possessed unusual ability as a mathematician.[59]
98. The chief work of the Cassel Observatory was the formation of a
star catalogue. The positions of stars were compared with that of
the sun, Venus or Jupiter being used as connecting links, and their
positions relatively to the equator and the first point of Aries
(♈) deduced; allowance was regularly made for the errors due to the
refraction of light by the atmosphere, as well as for the parallax of
the sun, but the most notable new departure was the use of a clock
to record the time of observations and to measure the motion of the
celestial sphere. The construction of clocks of sufficient accuracy for
the purpose was rendered possible by the mechanical genius of Bürgi,
and in particular by his discovery that a clock could be regulated by
a pendulum, a discovery which he appears to have taken no steps to
publish, and which had in consequence to be made again independently
before it received general recognition.[60] By 1586 121 stars had been
carefully observed, but a more extensive catalogue which was to have
contained more than a thousand stars was never finished, owing to the
unexpected disappearance of Rothmann in 1590[61] and the death of the
Landgrave two years later.
99. The work of the Cassel Observatory was, however, overshadowed by
that carried out nearly at the same time by _Tycho_ (_Tyge_) _Brahe_.
He was born in 1546 at Knudstrup in the Danish province of Scania
(now the southern extremity of Sweden), being the eldest child of a
nobleman who was afterwards governor of Helsingborg Castle. He was
adopted as an infant by an uncle, and brought up at his country estate.
When only 13 he went to the University of Copenhagen, where he began
to study rhetoric and philosophy, with a view to a political career.
He was, however, very much interested by a small eclipse of the sun
which he saw in 1560, and this stimulus, added to some taste for the
astrological art of casting horoscopes, led him to devote the greater
part of the remaining two years spent at Copenhagen to mathematics
and astronomy. In 1562 he went on to the University of Leipzig,
accompanied, according to the custom of the time, by a tutor, who
appears to have made persevering but unsuccessful attempts to induce
his pupil to devote himself to law. Tycho, however, was now as always
a difficult person to divert from his purpose, and went on steadily
with his astronomy. In 1563 he made his first recorded observation, of
a close approach of Jupiter and Saturn, the time of which he noticed
to be predicted a whole month wrong by the _Alfonsine Tables_ (chapter
III., § 66), while the _Prussian Tables_ (§ 94) were several days
in error. While at Leipzig he bought also a few rough instruments,
and anticipated one of the great improvements afterwards carried out
systematically, by trying to estimate and to allow for the errors of
his instruments.
In 1565 Tycho returned to Copenhagen, probably on account of the war
with Sweden which had just broken out, and stayed about a year, during
the course of which he lost his uncle. He then set out again (1566)
on his travels, and visited Wittenberg, Rostock, Basle, Ingolstadt,
Augsburg, and other centres of learning, thus making acquaintance with
several of the most notable astronomers of Germany. At Augsburg he
met the brothers Hainzel, rich citizens with a taste for science, for
one of whom he designed and had constructed an enormous =quadrant=
(quarter-circle) with a radius of about 19 feet, the rim of which was
graduated to single minutes; and he began also here the construction of
his great celestial globe, five feet in diameter, on which he marked
one by one the positions of the stars as he afterwards observed them.
In 1570 Tycho returned to his father at Helsingborg, and soon after
the death of the latter (1571) went for a long visit to Steen Bille,
an uncle with scientific tastes. During this visit he seems to have
devoted most of his time to chemistry (or perhaps rather to alchemy),
and his astronomical studies fell into abeyance for a time.
100. His interest in astronomy was fortunately revived by the
sudden appearance, in November 1572, of a brilliant new star in the
constellation Cassiopeia. Of this Tycho took a number of extremely
careful observations; he noted the gradual changes in its brilliancy
from its first appearance, when it rivalled Venus at her brightest,
down to its final disappearance 16 months later. He repeatedly measured
its angular distance from the chief stars in Cassiopeia, and applied
a variety of methods to ascertain whether it had any perceptible
parallax (chapter II., §§ 43, 49). No parallax could be definitely
detected, and he deduced accordingly that the star must certainly be
farther off than the moon; as moreover it had no share in the planetary
motions, he inferred that it must belong to the region of the fixed
stars. To us of to-day this result may appear fairly commonplace, but
most astronomers of the time held so firmly to Aristotle’s doctrine
that the heavens generally, and the region of the fixed stars in
particular, were incorruptible and unchangeable, that new stars
were, like comets, almost universally ascribed to the higher regions
of our own atmosphere. Tycho wrote an account of the new star, which
he was ultimately induced by his friends to publish (1573), together
with some portions of a calendar for that year which he had prepared.
His reluctance to publish appears to have been due in great part to
a belief that it was unworthy of the dignity of a Danish nobleman to
write books! The book in question (_De Nova ... Stella_) compares very
favourably with the numerous other writings which the star called
forth, though it shews that Tycho held the common beliefs that comets
were in our atmosphere, and that the planets were carried round by
solid crystalline spheres, two delusions which his subsequent work did
much to destroy. He also dealt at some length with the astrological
importance of the star, and the great events which it foreshadowed,
utterances on which Kepler subsequently made the very sensible
criticism that “if that star did nothing else, at least it announced
and produced a great astronomer.”
In 1574 Tycho was requested to give some astronomical lectures at
the University of Copenhagen, the first of which, dealing largely
with astrology, was printed in 1610, after his death. When these were
finished, he set off again on his travels (1575). After a short visit
to Cassel (§ 97), during which he laid the foundation of a lifelong
friendship with the Landgrave, he went on to Frankfort to buy books,
thence to Basle (where he had serious thoughts of settling) and on to
Venice, then back to Augsburg and to Regensburg, where he obtained a
copy of the _Commentariolus_ of Coppernicus (chapter IV., § 73), and
finally came home by way of Saalfeld and Wittenberg.
101. The next year (1576) was the beginning of a new epoch in Tycho’s
career. The King of Denmark, Frederick II., who was a zealous patron
of science and literature, determined to provide Tycho with endowments
sufficient to enable him to carry out his astronomical work in the most
effective way. He accordingly gave him for occupation the little island
of Hveen in the Sound (now belonging to Sweden), promised money for
building a house and observatory, and supplemented the income derived
from the rents of the island by an annual payment of about £100. Tycho
paid his first visit to the island in May, soon set to work building,
and had already begun to make regular observations in his new house
before the end of the year.
[Illustration: FIG. 51.—Uraniborg. From a collection of letters
published by Tycho.]
The buildings were as remarkable for their magnificence as for their
scientific utility. Tycho never forgot that he was a Danish nobleman as
well as an astronomer, and built in a manner suitable to his rank.[62]
His chief building (fig. 51), called Uraniborg (the Castle of the
Heavens), was in the middle of a large square enclosure, laid out as a
garden, the corners of which pointed North, East, South, and West, and
contained several observatories, a library and laboratory, in addition
to living rooms. Subsequently, when the number of pupils and assistants
who came to him had increased, he erected (1584) a second building,
Stjerneborg (Star Castle), which was remarkable for having underground
observatories. The convenience of being able to carry out all necessary
work on his own premises induced him moreover to establish workshops,
where nearly all his instruments were made, and afterwards also a
printing press and paper mill. Both at Uraniborg and Stjerneborg
not only the rooms, but even the instruments which were gradually
constructed, were elaborately painted or otherwise ornamented.
102. The expenses of the establishment must have been enormous,
particularly as Tycho lived in magnificent style and probably paid
little attention to economy. His income was derived from various
sources, and fluctuated from time to time, as the King did not merely
make him a fixed annual payment, but added also temporary grants of
lands or money. Amongst other benefactions he received in 1579 one of
the canonries of the cathedral of Roskilde, the endowments of which
had been practically secularised at the Reformation. Unfortunately
most of his property was held on tenures which involved corresponding
obligations, and as he combined the irritability of a genius with
the haughtiness of a mediaeval nobleman, continual quarrels were the
result. Very soon after his arrival at Hveen his tenants complained
of work which he illegally forced from them; chapel services which his
canonry required him to keep up were neglected, and he entirely refused
to make certain recognised payments to the widow of the previous canon.
Further difficulties arose out of a lighthouse, the maintenance of
which was a duty attached to one of his estates, but was regularly
neglected. Nothing shews the King’s good feeling towards Tycho more
than the trouble which he took to settle these quarrels, often ending
by paying the sum of money under dispute. Tycho was moreover extremely
jealous of his scientific reputation, and on more than one occasion
broke out into violent abuse of some assistant or visitor whom he
accused of stealing his ideas and publishing them elsewhere.
In addition to the time thus spent in quarrelling, a good deal must
have been occupied in entertaining the numerous visitors whom his
fame attracted, and who included, in addition to astronomers, persons
of rank such as several of the Danish royal family and James VI. of
Scotland (afterwards James I. of England).
Notwithstanding these distractions, astronomical work made steady
progress, and during the 21 years that Tycho spent at Hveen he
accumulated, with the help of pupils and assistants, a magnificent
series of observations, far transcending in accuracy and extent
anything that had been accomplished by his predecessors. A good deal of
attention was also given to alchemy, and some to medicine. He seems to
have been much impressed with the idea of the unity of Nature, and to
have been continually looking out for analogies or actual connection
between the different subjects which he studied.
103. In 1577 appeared a brilliant comet, which Tycho observed with
his customary care; and, although he had not at the time his full
complement of instruments, his observations were exact enough to
satisfy him that the comet was at least three times as far off as the
moon, and thus to refute the popular belief, which he had himself
held a few years before (§ 100), that comets were generated in our
atmosphere. His observations led him also to the belief that the comet
was revolving round the sun, at a distance from it greater than that
of Venus, a conclusion which interfered seriously with the common
doctrine of the solid crystalline spheres. He had further opportunities
of observing comets in 1580, 1582, 1585, 1590, and 1596, and one of his
pupils also took observations of a comet seen in 1593. None of these
comets attracted as much general attention as that of 1577, but Tycho’s
observations, as was natural, gradually improved in accuracy.
104. The valuable results obtained by means of the new star of 1572,
and by the comets, suggested the propriety of undertaking a complete
treatise on astronomy embodying these and other discoveries. According
to the original plan, there were to be three preliminary volumes
devoted respectively to the new star, to the comet of 1577, and to
the later comets, while the main treatise was to consist of several
more volumes dealing with the theories of the sun, moon, and planets.
Of this magnificent plan comparatively little was ever executed. The
first volume, called the _Astronomiae Instauratae Progymnasmata_, or
Introduction to the New Astronomy, was hardly begun till 1588, and,
although mostly printed by 1592, was never quite finished during
Tycho’s lifetime, and was actually published by Kepler in 1602. One
question, in fact, led to another in such a way that Tycho felt himself
unable to give a satisfactory account of the star of 1572 without
dealing with a number of preliminary topics, such as the positions of
the fixed stars, precession, and the annual motion of the sun, each
of which necessitated an elaborate investigation. The second volume,
dealing with the comet of 1577, called _De Mundi aetherei recentioribus
Phaenomenis Liber secundus_ (Second book about recent appearances in
the Celestial World), was finished long before the first, and copies
were sent to friends and correspondents in 1588, though it was not
regularly published and on sale till 1603. The third volume was never
written, though some material was collected for it, and the main
treatise does not appear to have been touched.
[Illustration: FIG. 52.—Tycho’s system of the world. From his book on
the comet of 1577.]
105. The book on the comet of 1577 is of special interest, as
containing an account of Tycho’s system of the world, which was a
compromise between those of Ptolemy and of Coppernicus. Tycho was too
good an astronomer not to realise many of the simplifications which
the Coppernican system introduced, but was unable to answer two of the
serious objections; he regarded any motion of “the sluggish and heavy
earth” as contrary to “physical principles,” and he objected to the
great distance of the stars which the Coppernican system required,
because a vast empty space would be left between them and the planets,
a space which he regarded as wasteful.[63] Biblical difficulties[64]
also had some weight with him. He accordingly devised (1583) a new
system according to which the five planets revolved round the sun (C,
in fig. 52), while the sun revolved annually round the earth (A), and
the whole celestial sphere performed also a daily revolution round
the earth. The system was never worked out in detail, and, like many
compromises, met with little support; Tycho nevertheless was extremely
proud of it, and one of the most violent and prolonged quarrels of
his life (lasting a dozen years) was with _Reymers Bär_ or _Ursus_
(?-1600), who had communicated to the Landgrave in 1586 and published
two years later a system of the world very like Tycho’s. Reymers had
been at Hveen for a short time in 1584, and Tycho had no hesitation in
accusing him of having stolen the idea from some manuscript seen there.
Reymers naturally retaliated with a counter-charge of theft against
Tycho. There is, however, no good reason why the idea should not have
occurred independently to each astronomer; and Reymers made in some
respects a great improvement on Tycho’s scheme by accepting the daily
rotation of the earth, and so doing away with the daily rotation of the
celestial sphere, which was certainly one of the weakest parts of the
Ptolemaic scheme.
[Illustration: TYCHO BRAHE.]
106. The same year (1588) which saw the publication of Tycho’s book on
the comet was also marked by the death of his patron, Frederick II.
The new King Christian was a boy of 11, and for some years the country
was managed by four leading statesmen. The new government seems to
have been at first quite friendly to Tycho; a large sum was paid to
him for expenses incurred at Hveen, and additional endowments were
promised, but as time went on Tycho’s usual quarrels with his tenants
and others began to produce their effect. In 1594 he lost one of
his chief supporters at court, the Chancellor Kaas, and his successor,
as well as two or three other important officials at court, were not
very friendly, although the stories commonly told of violent personal
animosities appear to have little foundation. As early as 1591 Tycho
had hinted to a correspondent that he might not remain permanently in
Denmark, and in 1594 he began a correspondence with representatives
of the Emperor Rudolph II., who was a patron of science. But his
scientific activity during these years was as great as ever; and in
1596 he completed the printing of an extremely interesting volume of
scientific correspondence between the Landgrave, Rothmann, and himself.
The accession of the young King to power in 1596 was at once followed
by the withdrawal of one of Tycho’s estates, and in the following year
the annual payment which had been made since 1576 was stopped. It is
difficult to blame the King for these economies; he was evidently
not as much interested in astronomy as his father, and consequently
regarded the heavy expenditure at Hveen as an extravagance, and it is
also probable that he was seriously annoyed at Tycho’s maltreatment of
his tenants, and at other pieces of unruly conduct on his part. Tycho,
however, regarded the forfeiture of his annual pension as the last
straw, and left Hveen early in 1597, taking his more portable property
with him. After a few months spent in Copenhagen, he took the decisive
step of leaving Denmark for Germany, in return for which action the
King deprived him of his canonry. Tycho thereupon wrote a remonstrance
in which he pointed out the impossibility of carrying on his work
without proper endowments, and offered to return if his services were
properly appreciated. The King, however, was by this time seriously
annoyed, and his reply was an enumeration of the various causes of
complaint against Tycho which had arisen of late years. Although Tycho
made some more attempts through various friends to regain royal favour,
the breach remained final.
107. Tycho spent the winter 1597-8 with a friend near Hamburg, and,
while there, issued, under the title of _Astronomiae Instauratae
Mechanica_, a description of his instruments, together with a short
autobiography and an interesting account of his chief discoveries.
About the same time he circulated manuscript copies of a catalogue of
1,000 fixed stars, of which only 777 had been properly observed, the
rest having been added hurriedly to make up the traditional number. The
catalogue and the _Mechanica_ were both intended largely as evidence
of his astronomical eminence, and were sent to various influential
persons. Negotiations went on both with the Emperor and with the Prince
of Orange, and after another year spent in various parts of Germany,
Tycho definitely accepted an invitation of the Emperor and arrived at
Prague in June 1599.
108. It was soon agreed that he should inhabit the castle of Benatek,
some twenty miles from Prague, where he accordingly settled with
his family and smaller instruments towards the end of 1599. He at
once started observing, sent one of his sons to Hveen for his larger
instruments, and began looking about for assistants. He secured one of
the most able of his old assistants, and by good fortune was also able
to attract a far greater man, _John Kepler_, to whose skilful use of
the materials collected by Tycho the latter owes no inconsiderable part
of his great reputation. Kepler, whose life and work will be dealt with
at length in chapter VII., had recently published his first important
work, the _Mysterium Cosmographicum_ (§ 136), which had attracted the
attention of Tycho among others, and was beginning to find his position
at Gratz in Styria uncomfortable on account of impending religious
disputes. After some hesitation he joined Tycho at Benatek early in
1600. He was soon set to work at the study of Mars for the planetary
tables which Tycho was then preparing, and thus acquired special
familiarity with the observations of this planet which Tycho had
accumulated. The relations of the two astronomers were not altogether
happy, Kepler being then as always anxious about money matters, and the
disturbed state of the country rendering it difficult for Tycho to get
payment from the Emperor. Consequently Kepler very soon left Benatek
and returned to Prague, where he definitely settled after a short visit
to Gratz; Tycho also moved there towards the end of 1600, and they then
worked together harmoniously for the short remainder of Tycho’s life.
Though he was by no means an old man, there were some indications that
his health was failing, and towards the end of 1601 he was suddenly
seized with an illness which terminated fatally after a few days
(November 24th). It is characteristic of his devotion to the great work
of his life that in the delirium which preceded his death he cried out
again and again his hope that his life might not prove to have been
fruitless (_Ne frustra vixisse videar_).
109. Partly owing to difficulties between Kepler and one of Tycho’s
family, partly owing to growing political disturbances, scarcely any
use was made of Tycho’s instruments after his death, and most of them
perished during the Civil Wars in Bohemia. Kepler obtained possession
of his observations; but they have never been published except in an
imperfect form.
110. Anything like a satisfactory account of Tycho’s services to
astronomy would necessarily deal largely with technical details of
methods of observing, which would be out of place here. It may,
however, be worth while to attempt to give some general account of his
characteristics as an observer before referring to special discoveries.
Tycho realised more fully than any of his predecessors the importance
of obtaining observations which should not only be as accurate as
possible, but should be taken so often as to preserve an almost
continuous record of the positions and motions of the celestial bodies
dealt with; whereas the prevailing custom (as illustrated for example
by Coppernicus) was only to take observations now and then, either
when an astronomical event of special interest such as an eclipse or a
conjunction was occurring, or to supply some particular datum required
for a point of theory. While Coppernicus, as has been already noticed
(chapter IV., § 73), only used altogether a few dozen observations in
his book, Tycho—to take one instance—observed the sun _daily_ for many
years, and must therefore have taken some thousands of observations
of this one body, in addition to the many thousands which he took of
other celestial bodies. It is true that the Arabs had some idea of
observing continuously (cf. chapter III., § 57), but they had too
little speculative power or originality to be able to make much use
of their observations, few of which passed into the hands of European
astronomers. Regiomontanus (chapter III., § 68), if he had lived, might
probably have to a considerable extent anticipated Tycho, but his
short life was too fully occupied with the study and interpretation of
Greek astronomy for him to accomplish very much in other departments
of the subject. The Landgrave and his staff, who were in constant
communication with Tycho, were working in the same direction, though on
the whole less effectively. Unlike the Arabs, Tycho was, however, fully
impressed with the idea that observations were only a means to an end,
and that mere observations without a hypothesis or theory to connect
and interpret them were of little use.
The actual accuracy obtained by Tycho in his observations naturally
varied considerably according to the nature of the observation, the
care taken, and the period of his career at which it was made. The
places which he assigned to nine stars which were fundamental in
his star catalogue differ from their positions as deduced from the
best modern observations by angles which are in most cases less than
1′, and in only one case as great as 2′ (this error being chiefly
due to refraction (chapter II., § 46), Tycho’s knowledge of which
was necessarily imperfect). Other star places were presumably less
accurate, but it will not be far from the truth if we assume that in
most cases the errors in Tycho’s observations did not exceed 1′ or 2′.
Kepler in a famous passage speaks of an error of 8′ in a planetary
observation by Tycho as impossible. This great increase in accuracy
can only be assigned in part to the size and careful construction of
the instruments used, the characteristics on which the Arabs and other
observers had laid such stress. Tycho certainly used good instruments,
but added very much to their efficiency, partly by minor mechanical
devices, such as the use of specially constructed “sights” and of a
particular method of graduation,[65] and partly by using instruments
capable only of restricted motions, and therefore of much greater
steadiness than instruments which were able to point to any part of
the sky. Another extremely important idea was that of systematically
allowing as far as possible for the inevitable mechanical imperfections
of even the best constructed instruments, as well as for other
permanent causes of error. It had been long known, for example, that
the refraction of light through the atmosphere had the effect of
slightly raising the apparent places of stars in the sky. Tycho took a
series of observations to ascertain the amount of this displacement for
different parts of the sky, hence constructed a table of refractions
(a very imperfect one, it is true), and in future observations
regularly allowed for the effect of refraction. Again, it was known
that observations of the sun and planets were liable to be disturbed
by the effect of parallax (chapter II., §§ 43, 49), though the amount
of this correction was uncertain. In cases where special accuracy was
required, Tycho accordingly observed the body in question at least
twice, choosing positions in which parallax was known to produce nearly
opposite effects, and thus by combining the observations obtained a
result nearly free from this particular source of error. He was also
one of the first to realise fully the importance of repeating the same
observation many times under different conditions, in order that the
various accidental sources of error in the separate observations should
as far as possible neutralise one another.
111. Almost every astronomical quantity of importance was re-determined
and generally corrected by him. The annual motion of the sun’s apogee
relative to ♈, for example, which Coppernicus had estimated at 24″,
Tycho fixed at 45″, the modern value being 61″; the length of
the year he determined with an error of less than a second; and he
constructed tables of the motion of the sun which gave its place to
within 1′, previous tables being occasionally 15′ or 20′ wrong. By an
unfortunate omission he made no inquiry into the distance of the sun,
but accepted the extremely inaccurate value which had been handed down,
without substantial alteration, from astronomer to astronomer since the
time of Hipparchus (chapter II., § 41).
In the theory of the moon Tycho made several important discoveries.
He found that the irregularities in its movement were not fully
represented by the equation of the centre and the evection (chapter
II., §§ 39, 48), but that there was a further irregularity which
vanished at opposition and conjunction as well as at quadratures,
but in intermediate positions of the moon might be as great as 40′.
This irregularity, known as the =variation=, was, as has been already
mentioned (chapter III., § 60), very possibly discovered by Abul Wafa,
though it had been entirely lost subsequently. At a later stage in
his career, at latest during his visit to Wittenberg in 1598-9, Tycho
found that it was necessary to introduce a further small inequality
known as the =annual equation=, which depended on the position of the
earth in its path round the sun; this, however, he never completely
investigated. He also ascertained that the inclination of the moon’s
orbit to the ecliptic was not, as had been thought, fixed, but
oscillated regularly, and that the motion of the moon’s nodes (chapter
II., § 40) was also variable.
112. Reference has already been made to the star catalogue. Its
construction led to a study of precession, the amount of which was
determined with considerable accuracy; the same investigation led Tycho
to reject the supposed irregularity in precession which, under the name
of trepidation (chapter III., § 58), had confused astronomy for several
centuries, but from this time forward rapidly lost its popularity.
The planets were always a favourite subject of study with Tycho, but
although he made a magnificent series of observations, of immense value
to his successors, he died before he could construct any satisfactory
theory of the planetary motions. He easily discovered, however, that
their motions deviated considerably from those assigned by any of the
planetary tables, and got as far as detecting some regularity in these
deviations.