<h1><SPAN name="ch-4" id="ch-4">Chapter IV.</SPAN></h1>
<h2>Kepler Joins Tycho.</h2>
<p>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 Tübingen 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.</p>
<p>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
<i>Theologus</i>, <i>Philosophicus</i>, <i>Medicus</i>, and <i>Mathematicus</i>, or whoever
else, having no laborious occupation entrusted to him, seeks his
pleasure <i>in studiis</i>, 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”.</p>
<p>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 <i>a priori</i> 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.</p>
<p>In 1606 came a second treatise on the new star, discussing various
theories to account for its appearance, and refusing to accept the
notion that it was a “fortuitous concourse of atoms”. This was followed
in 1607 by a treatise on comets, suggested by the comet appearing that
year, known as Halley’s comet after its next return. He regarded comets
as “planets” moving in straight lines, never having examined sufficient
observations of any comet to convince himself that their paths are
curved. If he had not assumed that they were external to the system and
so could not be expected to return, he might have anticipated Halley’s
discovery. Another suggestive remark of his was to the effect that the
planets must be self-luminous, as otherwise Mercury and Venus, at any
rate, ought to show phases. This was put to the test not long afterwards
by means of Galileo’s telescope.</p>
<p>In 1607 Kepler rushed into print with an alleged observation of Mercury
crossing the sun, but after Galileo’s discovery of sun-spots, Kepler at
once cheerfully retracted his observation of “Mercury,” and so far was
he from being annoyed or bigoted in his views, that he warmly adopted
Galileo’s side, in contrast to most of those whose opinions were liable
to be overthrown by the new discoveries. Maestlin and others of Kepler’s
friends took the opposite view.</p>
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