Kepler
Author: Walter W. Bryant
CONTENTS.
I. Astronomy Before Kepler
II. Early Life of Kepler
III. Tycho Brahe
IV. Kepler Joins Tycho
V. Kepler's Laws
VI. Closing Years
Appendix I.--List of Dates
Appendix II.--Bibliography
Glossary
CHAPTER I.
ASTRONOMY BEFORE KEPLER.
In order to emphasise the importance of the reforms introduced into
astronomy by Kepler, it will be well to sketch briefly the history of
the theories which he had to overthrow. In very early times it must have
been realised that the sun and moon were continually changing their
places among the stars. The day, the month, and the year were obvious
divisions of time, and longer periods were suggested by the tabulation
of eclipses. We can imagine the respect accorded to the Chaldaean sages
who first discovered that eclipses could be predicted, and how the
philosophers of Mesopotamia must have sought eagerly for evidence of
fresh periodic laws. Certain of the stars, which appeared to wander, and
were hence called planets, provided an extended field for these
speculations. Among the Chaldaeans and Babylonians the knowledge
gradually acquired was probably confined to the priests and utilised
mainly for astrological prediction or the fixing of religious
observances. Such speculations as were current among them, and also
among the Egyptians and others who came to share their knowledge, were
almost entirely devoted to mythology, assigning fanciful terrestrial
origins to constellations, with occasional controversies as to how the
earth is supported in space. The Greeks, too, had an elaborate mythology
largely adapted from their neighbours, but they were not satisfied with
this, and made persistent attempts to reduce the apparent motions of
celestial objects to geometrical laws. Some of the Pythagoreans, if not
Pythagoras himself, held that the earth is a sphere, and that the
apparent daily revolution of the sun and stars is really due to a motion
of the earth, though at first this motion of the earth was not supposed
to be one of rotation about an axis. These notions, and also that the
planets on the whole move round from west to east with reference to the
stars, were made known to a larger circle through the writings of Plato.
To Plato moreover is attributed the challenge to astronomers to
represent all the motions of the heavenly bodies by uniformly described
circles, a challenge generally held responsible for a vast amount of
wasted effort, and the postponement, for many centuries, of real
progress. Eudoxus of Cnidus, endeavouring to account for the fact that
the planets, during every apparent revolution round the earth, come to
rest twice, and in the shorter interval between these "stationary
points," move in the opposite direction, found that he could represent
the phenomena fairly well by a system of concentric spheres, each
rotating with its own velocity, and carrying its own particular planet
round its own equator, the outermost sphere carrying the fixed stars. It
was necessary to assume that the axes about which the various spheres
revolved should have circular motions also, and gradually an increased
number of spheres was evolved, the total number required by Aristotle
reaching fifty-five. It may be regarded as counting in Aristotle's
favour that he did consider the earth to be a sphere and not a flat
disc, but he seems to have thought that the mathematical spheres of
Eudoxus had a real solid existence, and that not only meteors, shooting
stars and aurora, but also comets and the milky way belong to the
atmosphere. His really great service to science in collating and
criticising all that was known of natural science would have been
greater if so much of the discussion had not been on the exact meaning
of words used to describe phenomena, instead of on the facts and causes
of the phenomena themselves.
Aristarchus of Samos seems to have been the first to suggest that the
planets revolved not about the earth but about the sun, but the idea
seemed so improbable that it was hardly noticed, especially as
Aristarchus himself did not expand it into a treatise.
About this time the necessity for more accurate places of the sun and
moon, and the liberality of the Ptolemys who ruled Egypt, combined to
provide regular observations at Alexandria, so that, when Hipparchus
came upon the scene, there was a considerable amount of material for him
to use. His discoveries marked a great advance in the science of
astronomy. He noted the irregular motion of the sun, and, to explain it,
assumed that it revolved uniformly not exactly about the earth but
about a point some distance away, called the "excentric".[1] The line
joining the centre of the earth to the excentric passes through the
apses of the sun's orbit, where its distance from the earth is greatest
and least. The same result he could obtain by assuming that the sun
moved round a small circle, whose centre described a larger circle about
the earth; this larger circle carrying the other was called the
"deferent": so that the actual motion of the sun was in an epicycle. Of
the two methods of expression Hipparchus ultimately preferred the
second. He applied the same process to the moon but found that he could
depend upon its being right only at new and full moon. The irregularity
at first and third quarters he left to be investigated by his
successors. He also considered the planetary observations at his
disposal insufficient and so gave up the attempt at a complete planetary
theory. He made improved determinations of some of the elements of the
motions of the sun and moon, and discovered the Precession of the
Equinoxes, from the Alexandrian observations which showed that each year
as the sun came to cross the equator at the vernal equinox it did so at
a point about fifty seconds of arc earlier on the ecliptic, thus
producing in 150 years an unmistakable change of a couple of degrees, or
four times the sun's diameter. He also invented trigonometry. His star
catalogue was due to the appearance of a new star which caused him to
search for possible previous similar phenomena, and also to prepare for
checking future ones. No advance was made in theoretical astronomy for
260 years, the interval between Hipparchus and Ptolemy of Alexandria.
Ptolemy accepted the spherical form of the earth but denied its rotation
or any other movement. He made no advance on Hipparchus in regard to the
sun, though the lapse of time had largely increased the errors of the
elements adopted by the latter. In the case of the moon, however,
Ptolemy traced the variable inequality noticed sometimes by Hipparchus
at first and last quarter, which vanished when the moon was in apogee or
perigee. This he called the evection, and introduced another epicycle
to represent it. In his planetary theory he found that the places given
by his adopted excentric did not fit, being one way at apogee and the
other at perigee; so that the centre of distance must be nearer the
earth. He found it best to assume the centre of distance half-way
between the centre of the earth and the excentric, thus "bisecting the
excentricity". Even this did not fit in the case of Mercury, and in
general the agreement between theory and observation was spoilt by the
necessity of making all the orbital planes pass through the centre of
the earth, instead of the sun, thus making a good accordance practically
impossible.
[Footnote 1: See Glossary for this and other technical terms.]
After Ptolemy's time very little was heard for many centuries of any
fresh planetary theory, though advances in some points of detail were
made, notably by some of the Arab philosophers, who obtained improved
values for some of the elements by using better instruments. From time
to time various modifications of Ptolemy's theory were suggested, but
none of any real value. The Moors in Spain did their share of the work
carried on by their Eastern co-religionists, and the first independent
star catalogue since the time of Hipparchus was made by another
Oriental, Tamerlane's grandson, Ulugh Begh, who built a fine observatory
at Samarcand in the fifteenth century. In Spain the work was not
monopolised by the Moors, for in the thirteenth century Alphonso of
Castile, with the assistance of Jewish and Christian computers, compiled
the Alphonsine tables, completed in 1252, in which year he ascended the
throne as Alphonso X. They were long circulated in MS. and were first
printed in 1483, not long before the end of the period of stagnation.
Copernicus was born in 1473 at Thorn in Polish Prussia. In the course of
his studies at Cracow and at several Italian universities, he learnt all
that was known of the Ptolemaic astronomy and determined to reform it.
His maternal uncle, the Bishop of Ermland, having provided him with a
lay canonry in the Cathedral of Frauenburg, he had leisure to devote
himself to Science. Reviewing the suggestions of the ancient Greeks, he
was struck by the simplification that would be introduced by reviving
the idea that the annual motion should be attributed to the earth itself
instead of having a separate annual epicycle for each planet and for the
sun. Of the seventy odd circles or epicycles required by the latest form
of the Ptolemaic system, Copernicus succeeded in dispensing with rather
more than half, but he still required thirty-four, which was the exact
number assumed before the time of Aristotle. His considerations were
almost entirely mathematical, his only invasion into physics being in
defence of the "moving earth" against the stock objection that if the
earth moved, loose objects would fly off, and towers fall. He did not
break sufficiently away from the old tradition of uniform circular
motion. Ptolemy's efforts at exactness were baulked, as we have seen, by
the supposed necessity of all the orbit planes passing through the
earth, and if Copernicus had simply transferred this responsibility to
the sun he would have done better. But he would not sacrifice the old
fetish, and so, the orbit of the earth being clearly not circular with
respect to the sun, he made all his planetary planes pass through the
centre of the earth's orbit, instead of through the sun, thus
handicapping himself in the same way though not in the same degree as
Ptolemy. His thirty-four circles or epicycles comprised four for the
earth, three for the moon, seven for Mercury (on account of his highly
eccentric orbit) and five each for the other planets.
It is rather an exaggeration to call the present accepted system the
Copernican system, as it is really due to Kepler, half a century after
the death of Copernicus, but much credit is due to the latter for his
successful attempt to provide a real alternative for the Ptolemaic
system, instead of tinkering with it. The old geocentric system once
shaken, the way was gradually smoothed for the heliocentric system,
which Copernicus, still hampered by tradition, did not quite reach. He
was hardly a practical astronomer in the observational sense. His first
recorded observation, of an occultation of Aldebaran, was made in 1497,
and he is not known to have made as many as fifty astronomical
observations, while, of the few he did make and use, at least one was
more than half a degree in error, which would have been intolerable to
such an observer as Hipparchus. Copernicus in fact seems to have
considered accurate observations unattainable with the instruments at
hand. He refused to give any opinion on the projected reform of the
calendar, on the ground that the motions of the sun and moon were not
known with sufficient accuracy. It is possible that with better data he
might have made much more progress. He was in no hurry to publish
anything, perhaps on account of possible opposition. Certainly Luther,
with his obstinate conviction of the verbal accuracy of the Scriptures,
rejected as mere folly the idea of a moving earth, and Melanchthon
thought such opinions should be prohibited, but Rheticus, a professor at
the Protestant University of Wittenberg and an enthusiastic pupil of
Copernicus, urged publication, and undertook to see the work through the
press. This, however, he was unable to complete and another Lutheran,
Osiander, to whom he entrusted it, wrote a preface, with the apparent
intention of disarming opposition, in which he stated that the
principles laid down were only abstract hypotheses convenient for
purposes of calculation. This unauthorised interpolation may have had
its share in postponing the prohibition of the book by the Church of
Rome.
According to Copernicus the earth is only a planet like the others, and
not even the biggest one, while the sun is the most important body in
the system, and the stars probably too far away for any motion of the
earth to affect their apparent places. The earth in fact is very small
in comparison with the distance of the stars, as evidenced by the fact
that an observer anywhere on the earth appears to be in the middle of
the universe. He shows that the revolution of the earth will account for
the seasons, and for the stationary points and retrograde motions of the
planets. He corrects definitely the order of the planets outwards from
the sun, a matter which had been in dispute. A notable defect is due to
the idea that a body can only revolve about another body or a point, as
if rigidly connected with it, so that, in order to keep the earth's axis
in a constant direction in space, he has to invent a third motion. His
discussion of precession, which he rightly attributes to a slow motion
of the earth's axis, is marred by the idea that the precession is
variable. With all its defects, partly due to reliance on bad
observations, the work showed a great advance in the interpretation of
the motions of the planets; and his determinations of the periods both
in relation to the earth and to the stars were adopted by Reinhold,
Professor of Astronomy at Wittenberg, for the new Prutenic or Prussian
Tables, which were to supersede the obsolete Alphonsine Tables of the
thirteenth century.
In comparison with the question of the motion of the earth, no other
astronomical detail of the time seems to be of much consequence. Comets,
such as from time to time appeared, bright enough for naked eye
observation, were still regarded as atmospheric phenomena, and their
principal interest, as well as that of eclipses and planetary
conjunctions, was in relation to astrology. Reform, however, was
obviously in the air. The doctrine of Copernicus was destined very soon
to divide others besides the Lutheran leaders. The leaven of inquiry was
working, and not long after the death of Copernicus real advances were
to come, first in the accuracy of observations, and, as a necessary
result of these, in the planetary theory itself.
CHAPTER II.
EARLY LIFE OF KEPLER.
On 21st December, 1571, at Weil in the Duchy of Wurtemberg, was born a
weak and sickly seven-months' child, to whom his parents Henry and
Catherine Kepler gave the name of John. Henry Kepler was a petty officer
in the service of the reigning Duke, and in 1576 joined the army serving
in the Netherlands. His wife followed him, leaving her young son in his
grandfather's care at Leonberg, where he barely recovered from a severe
attack of smallpox. It was from this place that John derived the
Latinised name of Leonmontanus, in accordance with the common practice
of the time, but he was not known by it to any great extent. He was sent
to school in 1577, but in the following year his father returned to
Germany, almost ruined by the absconding of an acquaintance for whom he
had become surety. Henry Kepler was obliged to sell his house and most
of his belongings, and to keep a tavern at Elmendingen, withdrawing his
son from school to help him with the rough work. In 1583 young Kepler
was sent to the school at Elmendingen, and in 1584 had another narrow
escape from death by a violent illness. In 1586 he was sent, at the
charges of the Duke, to the monastic school of Maulbronn; from whence,
in accordance with the school regulations, he passed at the end of his
first year the examination for the bachelor's degree at Tubingen,
returning for two more years as a "veteran" to Maulbronn before being
admitted as a resident student at Tubingen. The three years thus spent
at Maulbronn were marked by recurrences of several of the diseases from
which he had suffered in childhood, and also by family troubles at his
home. His father went away after a quarrel with his wife Catherine, and
died abroad. Catherine herself, who seems to have been of a very
unamiable disposition, next quarrelled with her own relatives. It is not
surprising therefore that Kepler after taking his M.A. degree in August,
1591, coming out second in the examination lists, was ready to accept
the first appointment offered him, even if it should involve leaving
home. This happened to be the lectureship in astronomy at Gratz, the
chief town in Styria. Kepler's knowledge of astronomy was limited to the
compulsory school course, nor had he as yet any particular leaning
towards the science; the post, moreover, was a meagre and unimportant
one. On the other hand he had frequently expressed disgust at the way in
which one after another of his companions had refused "foreign"
appointments which had been arranged for them under the Duke's scheme of
education. His tutors also strongly urged him to accept the lectureship,
and he had not the usual reluctance to leave home. He therefore
proceeded to Gratz, protesting that he did not thereby forfeit his claim
to a more promising opening, when such should appear. His astronomical
tutor, Maestlin, encouraged him to devote himself to his newly adopted
science, and the first result of this advice appeared before very long
in Kepler's "Mysterium Cosmographicum". The bent of his mind was towards
philosophical speculation, to which he had been attracted in his
youthful studies of Scaliger's "Exoteric Exercises". He says he devoted
much time "to the examination of the nature of heaven, of souls, of
genii, of the elements, of the essence of fire, of the cause of
fountains, the ebb and flow of the tides, the shape of the continents
and inland seas, and things of this sort". Following his tutor in his
admiration for the Copernican theory, he wrote an essay on the primary
motion, attributing it to the rotation of the earth, and this not for
the mathematical reasons brought forward by Copernicus, but, as he
himself says, on physical or metaphysical grounds. In 1595, having more
leisure from lectures, he turned his speculative mind to the number,
size, and motion of the planetary orbits. He first tried simple
numerical relations, but none of them appeared to be twice, thrice, or
four times as great as another, although he felt convinced that there
was some relation between the motions and the distances, seeing that
when a gap appeared in one series, there was a corresponding gap in the
other. These gaps he attempted to fill by hypothetical planets between
Mars and Jupiter, and between Mercury and Venus, but this method also
failed to provide the regular proportion which he sought, besides being
open to the objection that on the same principle there might be many
more equally invisible planets at either end of the series. He was
nevertheless unwilling to adopt the opinion of Rheticus that the number
six was sacred, maintaining that the "sacredness" of the number was of
much more recent date than the creation of the worlds, and could not
therefore account for it. He next tried an ingenious idea, comparing the
perpendiculars from different points of a quadrant of a circle on a
tangent at its extremity. The greatest of these, the tangent, not being
cut by the quadrant, he called the line of the sun, and associated with
infinite force. The shortest, being the point at the other end of the
quadrant, thus corresponded to the fixed stars or zero force;
intermediate ones were to be found proportional to the "forces" of the
six planets. After a great amount of unfinished trial calculations,
which took nearly a whole summer, he convinced himself that success did
not lie that way. In July, 1595, while lecturing on the great planetary
conjunctions, he drew quasi-triangles in a circular zodiac showing the
slow progression of these points of conjunction at intervals of just
over 240° or eight signs. The successive chords marked out a smaller
circle to which they were tangents, about half the diameter of the
zodiacal circle as drawn, and Kepler at once saw a similarity to the
orbits of Saturn and Jupiter, the radius of the inscribed circle of an
equilateral triangle being half that of the circumscribed circle. His
natural sequence of ideas impelled him to try a square, in the hope that
the circumscribed and inscribed circles might give him a similar
"analogy" for the orbits of Jupiter and Mars. He next tried a pentagon
and so on, but he soon noted that he would never reach the sun that way,
nor would he find any such limitation as six, the number of "possibles"
being obviously infinite. The actual planets moreover were not even six
but only five, so far as he knew, so he next pondered the question of
what sort of things these could be of which only five different figures
were possible and suddenly thought of the five regular solids.[2] He
immediately pounced upon this idea and ultimately evolved the following
scheme. "The earth is the sphere, the measure of all; round it describe
a dodecahedron; the sphere including this will be Mars. Round Mars
describe a tetrahedron; the sphere including this will be Jupiter.
Describe a cube round Jupiter; the sphere including this will be Saturn.
Now, inscribe in the earth an icosahedron, the sphere inscribed in it
will be Venus: inscribe an octahedron in Venus: the circle inscribed in
it will be Mercury." With this result Kepler was inordinately pleased,
and regretted not a moment of the time spent in obtaining it, though to
us this "Mysterium Cosmographicum" can only appear useless, even without
the more recent additions to the known planets. He admitted that a
certain thickness must be assigned to the intervening spheres to cover
the greatest and least distances of the several planets from the sun,
but even then some of the numbers obtained are not a very close fit for
the corresponding planetary orbits. Kepler's own suggested explanation
of the discordances was that they must be due to erroneous measures of
the planetary distances, and this, in those days of crude and infrequent
observations, could not easily be disproved. He next thought of a
variety of reasons why the five regular solids should occur in precisely
the order given and in no other, diverging from this into a subtle and
not very intelligible process of reasoning to account for the division
of the zodiac into 360°. The next subject was more important, and dealt
with the relation between the distances of the planets and their times
of revolution round the sun. It was obvious that the period was not
simply proportional to the distance, as the outer planets were all too
slow for this, and he concluded "either that the moving intelligences of
the planets are weakest in those that are farthest from the sun, or that
there is one moving intelligence in the sun, the common centre, forcing
them all round, but those most violently which are nearest, and that it
languishes in some sort and grows weaker at the most distant, because of
the remoteness and the attenuation of the virtue". This is not so near a
guess at the theory of gravitation as might be supposed, for Kepler
imagined that a repulsive force was necessary to account for the planets
being sometimes further from the sun, and so laid aside the idea of a
constant attractive force. He made several other attempts to find a law
connecting the distances and periods of the planets, but without success
at that time, and only desisted when by unconsciously arguing in a
circle he appeared to get the same result from two totally different
hypotheses. He sent copies of his book to several leading astronomers,
of whom Galileo praised his ingenuity and good faith, while Tycho Brahe
was evidently much struck with the work and advised him to adapt
something similar to the Tychonic system instead of the Copernican. He
also intimated that his Uraniborg observations would provide more
accurate determinations of the planetary orbits, and thus made Kepler
eager to visit him, a project which as we shall see was more than
fulfilled. Another copy of the book Kepler sent to Reymers the Imperial
astronomer with a most fulsome letter, which Tycho, who asserted that
Reymers had simply plagiarised his work, very strongly resented, thus
drawing from Kepler a long letter of apology. About the same time Kepler
had married a lady already twice widowed, and become involved in
difficulties with her relatives on financial grounds, and with the
Styrian authorities in connection with the religious disputes then
coming to a head. On account of these latter he thought it expedient,
the year after his marriage, to withdraw to Hungary, from whence he sent
short treatises to Tubingen, "On the magnet" (following the ideas of
Gilbert of Colchester), "On the cause of the obliquity of the ecliptic"
and "On the Divine wisdom as shown in the Creation". His next important
step makes it desirable to devote a chapter to a short notice of Tycho
Brahe.
[Footnote 2: Since the sum of the plane angles at a corner of a regular
solid must be less than four right angles, it is easily seen that few
regular solids are possible. Hexagonal faces are clearly impossible, or
any polygonal faces with more than five sides. The possible forms are
the dodecahedron with twelve pentagonal faces, three meeting at each
corner; the cube, six square faces, three meeting at each corner; and
three figures with triangular faces, the tetrahedron of four faces,
three meeting at each corner; the octahedron of eight faces, four
meeting at each corner; and the icosahedron of twenty faces, five
meeting at each corner.]
CHAPTER III.
TYCHO BRAHE.
The age following that of Copernicus produced three outstanding figures
associated with the science of astronomy, then reaching the close of
what Professor Forbes so aptly styles the geometrical period. These
three Sir David Brewster has termed "Martyrs of Science"; Galileo, the
great Italian philosopher, has his own place among the "Pioneers of
Science"; and invaluable though Tycho Brahe's work was, the latter can
hardly be claimed as a pioneer in the same sense as the other two.
Nevertheless, Kepler, the third member of the trio, could not have made
his most valuable discoveries without Tycho's observations.
Of noble family, born a twin on 14th December, 1546, at Knudstrup in
Scania (the southernmost part of Sweden, then forming part of the
kingdom of Denmark), Tycho was kidnapped a year later by a childless
uncle. This uncle brought him up as his own son, provided him at the age
of seven with a tutor, and sent him in 1559 to the University of
Copenhagen, to study for a political career by taking courses in
rhetoric and philosophy. On 21st August, 1560, however, a solar eclipse
took place, total in Portugal, and therefore of small proportions in
Denmark, and Tycho's keen interest was awakened, not so much by the
phenomenon, as by the fact that it had occurred according to prediction.
Soon afterwards he purchased an edition of Ptolemy in order to read up
the subject of astronomy, to which, and to mathematics, he devoted most
of the remainder of his three years' course at Copenhagen. His uncle
next sent him to Leipzig to study law, but he managed to continue his
astronomical researches. He obtained the Alphonsine and the new Prutenic
Tables, but soon found that the latter, though more accurate than the
former, failed to represent the true positions of the planets, and
grasped the fact that continuous observation was essential in order to
determine the true motions. He began by observing a conjunction of
Jupiter and Saturn in August, 1563, and found the Prutenic Tables
several days in error, and the Alphonsine a whole month. He provided
himself with a cross-staff for determining the angular distance between
stars or other objects, and, finding the divisions of the scale
inaccurate, constructed a table of corrections, an improvement that
seems to have been a decided innovation, the previous practice having
been to use the best available instrument and ignore its errors. About
this time war broke out between Denmark and Sweden, and Tycho returned
to his uncle, who was vice-admiral and attached to the king's suite. The
uncle died in the following month, and early in the next year Tycho went
abroad again, this time to Wittenberg. After five months, however, an
outbreak of plague drove him away, and he matriculated at Rostock, where
he found little astronomy but a good deal of astrology. While there he
fought a duel in the dark and lost part of his nose, which he replaced
by a composition of gold and silver. He carried on regular observations
with his cross-staff and persevered with his astronomical studies in
spite of the objections and want of sympathy of his fellow-countrymen.
The King of Denmark, however, having a higher opinion of the value of
science, promised Tycho the first canonry that should fall vacant in the
cathedral chapter of Roskilde, so that he might be assured of an income
while devoting himself to financially unproductive work. In 1568 Tycho
left Rostock, and matriculated at Basle, but soon moved on to Augsburg,
where he found more enthusiasm for astronomy, and induced one of his new
friends to order the construction of a large 19-foot quadrant of heavy
oak beams. This was the first of the series of great instruments
associated with Tycho's name, and it remained in use for five years,
being destroyed by a great storm in 1574. Tycho meanwhile had left
Augsburg in 1570 and returned to live with his father, now governor of
Helsingborg Castle, until the latter's death in the following year.
Tycho then joined his mother's brother, Steen Bille, the only one of his
relatives who showed any sympathy with his desire for a scientific
career.
On 11th November, 1572, Tycho noticed an unfamiliar bright star in the
constellation of Cassiopeia, and continued to observe it with a sextant.
It was a very brilliant object, equal to Venus at its brightest for the
rest of November, not falling below the first magnitude for another four
months, and remaining visible for more than a year afterwards. Tycho
wrote a little book on the new star, maintaining that it had practically
no parallax, and therefore could not be, as some supposed, a comet.
Deeming authorship beneath the dignity of a noble he was very reluctant
to publish, but he was convinced of the importance of increasing the
number and accuracy of observations, though he was by no means free from
all the erroneous ideas of his time. The little book contained a certain
amount of astrology, but Tycho evidently did not regard this as of very
great importance. He adopted the view that the very rarity of the
phenomenon of a new star must prevent the formulation and adoption of
definite rules for determining its significance. We gather from lectures
which he was persuaded to deliver at the University of Copenhagen that,
though in agreement with the accepted canons of astrology as to the
influence of planetary conjunctions and such phenomena on the course of
human events, he did not consider the fate predicted by anyone's
horoscope to be unavoidable, but thought the great value of astrology
lay in the warnings derived from such computations, which should enable
the believer to avoid threatened calamities. In 1575 he left Denmark
once more and made his way to Cassel, where he found a kindred spirit in
the studious Landgrave, William IV. of Hesse, whose astronomical
pursuits had been interrupted by his accession to the government of
Hesse, in 1567. Tycho observed with him for some time, the two forming a
firm friendship, and then visited successively Frankfort, Basle, and
Venice, returning by way of Augsburg, Ratisbon, and Saalfeld to
Wittenberg; on the way he acquired various astronomical manuscripts,
made friends among practical astronomers, and examined new instruments.
He seemed to have considered the advantages of the several places thus
visited and decided on Basle, but on his return to Denmark to fetch his
family with the object of transferring them to Basle, he found that his
friend the Landgrave had written to King Frederick on his behalf,
urging him to provide the means to enable Tycho to pursue his
astronomical work, promising that not only should credit result for the
king and for Denmark but that science itself would be greatly advanced.
The ultimate result of this letter was that after refusing various
offers, Tycho accepted from the king a grant of the small island of
Hveen, in the Sound, with a guaranteed income, in addition to a large
sum from the treasury for building an observatory on the island, far
removed from the distractions of court life. Here Tycho built his
celebrated observatory of Uraniborg and began observations in December,
1576, using the large instruments then found necessary in order to
attain the accuracy of observation which within the next half-century
was to be so greatly facilitated by the invention of the telescope. Here
also he built several smaller observing rooms, so that his pupils should
be able to observe independently. For more than twenty years he
continued his observations at Uraniborg, surrounded by his family, and
attracting numerous pupils. His constant aim was to accumulate a large
store of observations of a high order of accuracy, and thus to provide
data for the complete reform of astronomy. As we have seen, few of the
Danish nobles had any sympathy with Tycho's pursuits, and most of them
strongly resented the continual expense borne by the King's treasury.
Tycho moreover was so absorbed in his scientific pursuits that he would
not take the trouble to be a good landlord, nor to carry out all the
duties laid upon him in return for certain of his grants of income. His
buildings included a chemical laboratory, and he was in the habit of
making up elixirs for various medical purposes; these were quite
popular, particularly as he made no charge for them. He seems to have
been something of a homoeopathist, for he recommends sulphur to cure
infectious diseases "brought on by the sulphurous vapours of the Aurora
Borealis"!
King Frederick, in consideration of various grants to Tycho, relied
upon his assistance in scientific matters, and especially in
astrological calculations; such as the horoscope of the heir apparent,
Prince Christian, born in 1577, which has been preserved among Tycho's
writings. There is, however, no known copy in existence of any of the
series of annual almanacs with predictions which he prepared for the
King. In November, 1577, appeared a bright comet, which Tycho carefully
observed with his sextant, proving that it had no perceptible parallax,
and must therefore be further off than the moon. He thus definitely
overthrew the common belief in the atmospheric origin of comets, which
he had himself hitherto shared. With increasing accuracy he observed
several other comets, notably one in 1585, when he had a full equipment
of instruments and a large staff of assistants. The year 1588, which saw
the death of his royal benefactor, saw also the publication of a volume
of Tycho's great work "Introduction to the New Astronomy". The first
volume, devoted to the new star of 1572, was not ready, because the
reduction of the observations involved so much research to correct the
star places for refraction, precession, etc.; it was not completed in
fact until Tycho's death, but the second volume, dealing with the comet
of 1577, was printed at Uraniborg and some copies were issued in 1588.
Besides the comet observations it included an account of Tycho's system
of the world. He would not accept the Copernican system, as he
considered the earth too heavy and sluggish to move, and also that the
authority of Scripture was against such an hypothesis. He therefore
assumed that the other planets revolved about the sun, while the sun,
moon, and stars revolved about the earth as a centre. Geometrically this
is much the same as the Copernican system, but physically it involves
the grotesque demand that the whole system of stars revolves round our
insignificant little earth every twenty-four hours. Since his previous
small book on the comet, Tycho had evidently considered more fully its
possible astrological significance, for he foretold a religious war,
giving the date of its commencement, and also the rising of a great
Protestant champion. These predictions were apparently fulfilled almost
to the letter by the great religious wars that broke out towards the end
of the sixteenth century, and in the person of Gustavus Adolphus.
King Frederick's death did not at first affect Tycho's position, for the
new king, Christian, was only eleven years old, and for some years the
council of regents included two of his supporters. After their deaths,
however, his emoluments began to be cut down on the plea of economy, and
as he took very little trouble to carry out any other than scientific
duties it was easy enough for his enemies to find fault. One after
another source of income was cut off, but he persevered with his
scientific work, including a catalogue of stars. He had obtained plenty
of good observations of 777 stars, but thought his catalogue should
contain 1000 stars, so he hastily observed as many more as he could up
to the time of his leaving Hveen, though even then he had not completed
his programme. About the time that King Christian reached the age of
eighteen, Tycho began to look about for a new patron, and to consider
the prospects offered by transferring himself with his instruments and
activities to the patronage of the Emperor Rudolph II. In 1597, when
even his pension from the Royal treasury was cut off, he hurriedly
packed up his instruments and library, and after a few weeks' sojourn at
Copenhagen, proceeded to Rostock, in Mecklenburg, whence he sent an
appeal to King Christian. It is possible that had he done this before
leaving Hveen it might have had more effect, but it can be readily seen
from the tone of the king's unfavourable reply that his departure was
regarded as an aggravation of previous shortcomings. Driven from Rostock
by the plague, Tycho settled temporarily at Wandsbeck, in Holstein, but
towards the end of 1598 set out to meet the Emperor at Prague. Once
more plague intervened and he spent some time at Dresden, afterwards
going to Wittenberg for the winter. He ultimately reached Prague in
June, 1599. Rudolph granted him a salary of at least 3000 florins,
promising also to settle on him the first hereditary estate that should
lapse to the Crown. He offered, moreover, the choice between three
castles outside Prague, of which Tycho chose Benatek. There he set about
altering the buildings in readiness for his instruments, for which he
sent to Uraniborg. Before they reached him, after many vexatious delays,
he had given up waiting for the funds promised for his building
expenses, and removed from Benatek to Prague. It was during this
interval that after considerable negotiation, Kepler, who had been in
correspondence with Tycho, consented to join him as an assistant.
Another assistant, Longomontanus, who had been with Tycho at Uraniborg,
was finding difficulty with the long series of Mars observations, and it
was arranged that he should transfer his energies to the lunar
observations, leaving those of Mars for Kepler. Before very much could
be done with them, however, Tycho died at the end of October, 1601. He
may have regretted the peaceful island of Hveen, considering the
troubles in which Bohemia was rapidly becoming involved, but there is
little doubt that had it not been for his self-imposed exile, his
observations would not have come into Kepler's hands, and their great
value might have been lost. In any case it was at Uraniborg that the
mass of observations was produced upon which the fame of Tycho Brahe
rests. His own discoveries, though in themselves the most important made
in astronomy for many centuries, are far less valuable than those for
which his observations furnished the material. He discovered the third
and fourth inequalities of the moon in longitude, called respectively
the variation and the annual equation, also the variability of the
motion of the moon's nodes and the inclination of its orbit to the
ecliptic. He obtained an improved value of the constant of precession,
and did good service by rejecting the idea that it was variable, an idea
which, under the name of trepidation, had for many centuries been
accepted. He discovered the effect of refraction, though only
approximately its amount, and determined improved values of many other
astronomical constants, but singularly enough made no determination of
the distance of the sun, adopting instead the ancient and erroneous
value given by Hipparchus.
His magnificent Observatory of Uraniborg, the finest building for
astronomical purposes that the world had hitherto seen, was allowed to
fall into decay, and scarcely more than mere indications of the site may
now be seen.
CHAPTER IV.
KEPLER JOINS TYCHO.
The association of Kepler with Tycho was one of the most important
landmarks in the history of astronomy. The younger man hoped, by the aid
of Tycho's planetary observations, to obtain better support for some of
his fanciful speculative theories, while the latter, who had certainly
not gained in prestige by leaving Denmark, was in great need of a
competent staff of assistants. Of the two it would almost seem that
Tycho thought himself the greater gainer, for in spite of his reputation
for brusqueness and want of consideration, he not only made light of
Kepler's apology in the matter of Reymers, but treated him with uniform
kindness in the face of great rudeness and ingratitude. He begged him to
come "as a welcome friend," though Kepler, very touchy on the subject of
his own astronomical powers, was afraid he might be regarded as simply a
subordinate assistant. An arrangement had been suggested by which Kepler
should obtain two years' leave of absence from Gratz on full pay, which,
because of the higher cost of living in Prague, should be supplemented
by the Emperor; but before this could be concluded, Kepler threw up his
professorship, and thinking he had thereby also lost the chance of going
to Prague, applied to Maestlin and others of his Tubingen friends to
make interest for him with the Duke of Wurtemberg and secure the
professorship of medicine. Tycho, however, still urged him to come to
Prague, promising to do his utmost to secure for him a permanent
appointment, or in any event to see that he was not the loser by coming.
Kepler was delayed by illness on the way, but ultimately reached Prague,
accompanied by his wife, and for some time lived entirely at Tycho's
expense, writing by way of return essays against Reymers and another
man, who had claimed the credit of the Tychonic system. This Kepler
could do with a clear conscience, as it was only a question of priority
and did not involve any support of the system, which he deemed far
inferior to that of Copernicus. The following year saw friction between
the two astronomers, and we learn from Kepler's abject letter of apology
that he was entirely in the wrong. It was about money matters, which in
one way or another embittered the rest of Kepler's life, and it arose
during his absence from Prague. On his return in September, 1601, Tycho
presented him to the Emperor, who gave him the title of Imperial
Mathematician, on condition of assisting Tycho in his calculations, the
very thing Kepler was most anxious to be allowed to do: for nowhere else
in the world was there such a collection of good observations sufficient
for his purpose of reforming the whole theory of astronomy. The
Emperor's interest was still mainly with astrology, but he liked to
think that his name would be handed down to posterity in connection
with the new Planetary Tables in the same way as that of Alphonso of
Castile, and he made liberal promises to pay the expenses. Tycho's other
principal assistant, Longomontanus, did not stay long after giving up
the Mars observations to Kepler, but instead of working at the new lunar
theory, suddenly left to take up a professorship of astronomy in his
native Denmark. Very shortly afterwards Tycho himself died of acute
distemper; Kepler began to prepare the mass of manuscripts for
publication, but, as everything was claimed by the Brahe family, he was
not allowed to finish the work. He succeeded to Tycho's post of
principal mathematician to the Emperor, at a reduced official salary,
which owing to the emptiness of the Imperial treasury was almost always
in arrear. In order to meet his expenses he had recourse to the casting
of nativities, for which he gained considerable reputation and received
very good pay. He worked by the conventional rules of astrology, and was
quite prepared to take fees for so doing, although he had very little
faith in them, preferring his own fanciful ideas.
In 1604 the constellation of Cassiopeia was once more temporarily
enriched by the appearance of a new star, said by some to be brighter
than Tycho's nova, and by others to be twice as bright as Jupiter.
Kepler at once wrote a short account of it, from which may be gathered
some idea of his attitude towards astrology. Contrasting the two novae,
he says: "Yonder one chose for its appearance a time no way remarkable,
and came into the world quite unexpectedly, like an enemy storming a
town and breaking into the market-place before the citizens are aware of
his approach; but ours has come exactly in the year of which astrologers
have written so much about the fiery trigon that happens in it; just in
the month in which (according to Cyprian), Mars comes up to a very
perfect conjunction with the other two superior planets; just in the day
when Mars has joined Jupiter, and just in the region where this
conjunction has taken place. Therefore the apparition of this star is
not like a secret hostile irruption, as was that one of 1572, but the
spectacle of a public triumph, or the entry of a mighty potentate; when
the couriers ride in some time before to prepare his lodgings, and the
crowd of young urchins begin to think the time over long to wait, then
roll in, one after another, the ammunition and money, and baggage
waggons, and presently the trampling of horse and the rush of people
from every side to the streets and windows; and when the crowd have
gazed with their jaws all agape at the troops of knights; then at last
the trumpeters and archers and lackeys so distinguish the person of the
monarch, that there is no occasion to point him out, but every one cries
of his own accord--'Here we have him'. What it may portend is hard to
determine, and this much only is certain, that it comes to tell mankind
either nothing at all or high and mighty news, quite beyond human sense
and understanding. It will have an important influence on political and
social relations; not indeed by its own nature, but as it were
accidentally through the disposition of mankind. First, it portends to
the booksellers great disturbances and tolerable gains; for almost every
_Theologus_, _Philosophicus_, _Medicus_, and _Mathematicus_, or whoever
else, having no laborious occupation entrusted to him, seeks his
pleasure _in studiis_, will make particular remarks upon it, and will
wish to bring these remarks to the light. Just so will others, learned
and unlearned, wish to know its meaning, and they will buy the authors
who profess to tell them. I mention these things merely by way of
example, because although thus much can be easily predicted without
great skill, yet may it happen just as easily, and in the same manner,
that the vulgar, or whoever else is of easy faith, or, it may be, crazy,
may wish to exalt himself into a great prophet; or it may even happen
that some powerful lord, who has good foundation and beginning of great
dignities, will be cheered on by this phenomenon to venture on some new
scheme, just as if God had set up this star in the darkness merely to
enlighten them." He made no secret of his views on conventional
astrology, as to which he claimed to speak with the authority of one
fully conversant with its principles, but he nevertheless expressed his
sincere conviction that the conjunctions and aspects of the planets
certainly did affect things on the earth, maintaining that he was driven
to this belief against his will by "most unfailing experiences".
Meanwhile the projected Rudolphine Tables were continually delayed by
the want of money. Kepler's nominal salary should have been ample for
his expenses, increased though they were by his growing family, but in
the depleted state of the treasury there were many who objected to any
payment for such "unpractical" purposes. This particular attitude has
not been confined to any special epoch or country, but the obvious
result in Kepler's case was to compel him to apply himself to less
expensive matters than the Planetary Tables, and among these must be
included not only the horoscopes or nativities, which owing to his
reputation were always in demand, but also other writings which probably
did not pay so well. In 1604 he published "A Supplement to Vitellion,"
containing the earliest known reasonable theory of optics, and
especially of dioptrics or vision through lenses. He compared the
mechanism of the eye with that of Porta's "Camera Obscura," but made no
attempt to explain how the image formed on the retina is understood by
the brain. He went carefully into the question of refraction, the
importance of which Tycho had been the first astronomer to recognise,
though he only applied it at low altitudes, and had not arrived at a
true theory or accurate values. Kepler wasted a good deal of time and
ingenuity on trial theories. He would invariably start with some
hypothesis, and work out the effect. He would then test it by
experiment, and when it failed would at once recognise that his
hypothesis was _a priori_ bound to fail. He rarely seems to have noticed
the fatal objections in time to save himself trouble. He would then at
once start again on a new hypothesis, equally gratuitous and equally
unfounded. It never seems to have occurred to him that there might be a
better way of approaching a problem. Among the lines he followed in this
particular investigation were, first, that refraction depends only on
the angle of incidence, which, he says, cannot be correct as it would
thus be the same for all refracting substances; next, that it depended
also on the density of the medium. This was a good shot, but he
unfortunately assumed that all rays passing into a denser medium would
apparently penetrate it to a depth depending only on the medium, which
means that there is a constant ratio between the tangents, instead of
the sines, of the inclination of the incident and refracted rays to the
normal. Experiment proved that this gave too high values for refraction
near the vertical compared with those near the horizon, so Kepler "went
off at a tangent" and tried a totally new set of ideas, which all
reduced to the absurdity of a refraction which vanished at the horizon.
These were followed by another set, involving either a constant amount
of refraction or one becoming infinite. He then came to the conclusion
that these geometrical methods must fail because the refracted image is
not real, and determined to try by analogy only, comparing the equally
unreal image formed by a mirror with that formed by refraction in water.
He noticed how the bottom of a vessel containing water appears to rise
more and more away from the vertical, and at once jumped to the analogy
of a concave mirror, which magnifies the image, while a convex mirror
was likened to a rarer medium. This line of attack also failed him, as
did various attempts to find relations between his measurements of
refraction and conic sections, and he broke off suddenly with a diatribe
against Tycho's critics, whom he likened to blind men disputing about
colours. Not many years later Snell discovered the true law of
refraction, but Kepler's contribution to the subject, though he failed
to discover the actual law, includes several of the adopted "by-laws".
He noted that atmospheric refraction would alter with the height of the
atmosphere and with temperature, and also recognised the fact that
rainbow colours depend on the angle of refraction, whether seen in the
rainbow itself, or in dew, glass, water, or any similar medium. He thus
came near to anticipating Newton. Before leaving the subject of Kepler's
optics it will be well to recall that a few years later after hearing of
Galileo's telescope, Kepler suggested that for astronomical purposes two
convex lenses should be used, so that there should be a real image where
measuring wires could be placed for reference. He did not carry out the
idea himself, and it was left to the Englishman Gascoigne to produce the
first instrument on this "Keplerian" principle, universally known as the Astronomical Telescope. |
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