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 Tübingen,
returning for two more years as a "veteran" to Maulbronn before being
admitted as a resident student at Tübingen. 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 Tübingen, "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.]