KEPLER.
“His celebrated laws were the outcome of a lifetime of speculation,
for the most part vain and groundless.... But Kepler’s name was
destined to be immortal, on account of the patience with which he
submitted his hypotheses to comparison with observation, the candour
with which he acknowledged failure after failure, and the perseverance
and ingenuity with which he renewed his attack upon the riddles of
nature.”
JEVONS.
135. John Kepler, or Keppler,[83] was born in 1571, seven years
after Galilei, at Weil in Würtemberg; his parents were in reduced
circumstances, though his father had some claims to noble descent.
Though Weil itself was predominantly Roman Catholic, the Keplers were
Protestants, a fact which frequently stood in Kepler’s way at various
stages of his career. But the father could have been by no means
zealous in his faith, for he enlisted in the army of the notorious Duke
of Alva when it was engaged in trying to suppress the revolt of the
Netherlands against Spanish persecution.
John Kepler’s childhood was marked by more than the usual number of
illnesses, and his bodily weaknesses, combined with a promise of great
intellectual ability, seemed to point to the Church as a suitable
career for him. After attending various elementary schools with great
irregularity—due partly to ill-health, partly to the requirements of
manual work at home—he was sent in 1584 at the public expense to the
monastic school at Adelberg, and two years later to the more advanced
school or college of the same kind at Maulbronn, which was connected
with the University of Tübingen, then one of the great centres of
Protestant theology.
In 1588 he obtained the B.A. degree, and in the following year entered
the philosophical faculty at Tübingen.
There he came under the influence of Maestlin, the professor of
mathematics, by whom he was in private taught the principles of the
Coppernican system, though the professorial lectures were still on the
traditional lines.
In 1591 Kepler graduated as M.A., being second out of fourteen
candidates, and then devoted himself chiefly to the study of theology.
136. In 1594, however, the Protestant Estates of Styria applied to
Tübingen for a lecturer on mathematics (including astronomy) for the
high school of Gratz, and the appointment was offered to Kepler. Having
no special knowledge of the subject and as yet no taste for it, he
naturally hesitated about accepting the offer, but finally decided
to do so, expressly stipulating, however, that he should not thereby
forfeit his claims to ecclesiastical preferment in Würtemberg. The
demand for higher mathematics at Gratz seems to have been slight;
during his first year Kepler’s mathematical lectures were attended
by very few students, and in the following year by none, so that to
prevent his salary from being wasted he was set to teach the elements
of various other subjects. It was moreover one of his duties to
prepare an annual almanack or calendar, which was expected to contain
not merely the usual elementary astronomical information such as we
are accustomed to in the calendars of to-day, but also astrological
information of a more interesting character, such as predictions of
the weather and of remarkable events, guidance as to unlucky and lucky
times, and the like. Kepler’s first calendar, for the year 1595,
contained some happy weather-prophecies, and he acquired accordingly
a considerable popular reputation as a prophet and astrologer, which
remained throughout his life.
Meanwhile his official duties evidently left him a good deal of
leisure, which he spent with characteristic energy in acquiring as
thorough a knowledge as possible of astronomy, and in speculating on
the subject.
According to his own statement, “there were three things in particular,
_viz._ the number, the size, and the motion of the heavenly bodies,
as to which he searched zealously for reasons why they were as they
were and not otherwise”; and the results of a long course of wild
speculation on the subject led him at last to a result with which he
was immensely pleased—a numerical relation connecting the distances
of the several planets from the sun with certain geometrical bodies
known as the regular solids (of which the cube is the best known), a
relation which is not very accurate numerically, and is of absolutely
no significance or importance.[84] This discovery, together with a
detailed account of the steps which led to it, as well as of a number
of other steps which led nowhere, was published in 1596 in a book a
portion of the title of which may be translated as _The Forerunner of
Dissertations on the Universe, containing the Mystery of the Universe_,
commonly referred to as the _Mysterium Cosmographicum_. The contents
were probably much more attractive and seemed more valuable to Kepler’s
contemporaries than to us, but even to those who were least inclined
to attach weight to its conclusions, the book shewed evidence of
considerable astronomical knowledge and very great ingenuity; and both
Tycho Brahe and Galilei, to whom copies were sent, recognised in the
author a rising astronomer likely to do good work.
137. In 1597 Kepler married. In the following year the religious
troubles, which had for some years been steadily growing, were
increased by the action of the Archduke Ferdinand of Austria
(afterwards the Emperor Ferdinand II.), who on his return from a
pilgrimage to Loretto started a vigorous persecution of Protestants
in his dominions, one step in which was an order that all Protestant
ministers and teachers in Styria should quit the country at once
(1598). Kepler accordingly fled to Hungary, but returned after a
few weeks by special permission of the Archduke, given apparently
on the advice of the Jesuit party, who had hopes of converting the
astronomer. Kepler’s hearers had, however, mostly been scattered by
the persecution, it became difficult to ensure regular payment of
his stipend, and the rising tide of Catholicism made his position
increasingly insecure. Tycho’s overtures were accordingly welcome,
and in 1600 he paid a visit to him, as already described (chapter V.,
§ 108), at Benatek and Prague. He returned to Gratz in the autumn,
still uncertain whether to accept Tycho’s offer or not, but being then
definitely dismissed from his position at Gratz on account of his
Protestant opinions, he returned finally to Prague at the end of the
year.
138. Soon after Tycho’s death Kepler was appointed his successor as
mathematician to the Emperor Rudolph (1602), but at only half his
predecessor’s salary, and even this was paid with great irregularity,
so that complaints as to arrears and constant pecuniary difficulties
played an important part in his future life, as they had done during
the later years at Gratz. Tycho’s instruments never passed into his
possession, but as he had little taste or skill for observing, the loss
was probably not great; fortunately, after some difficulties with the
heirs, he secured control of the greater part of Tycho’s incomparable
series of observations, the working up of which into an improved theory
of the solar system was the main occupation of the next 25 years of
his life. Before, however, he had achieved any substantial result in
this direction, he published several minor works—for example, two
pamphlets on a new star which appeared in 1604, and a treatise on
the applications of optics to astronomy (published in 1604 with a
title beginning _Ad Vitellionem Paralipomena quibus Astronomiae Pars
Optica Traditur_ ...), the most interesting and important part of
which was a considerable improvement in the theory of astronomical
refraction (chapter II., § 46, and chapter V., § 110). A later optical
treatise (the _Dioptrice_ of 1611) contained a suggestion for the
construction of a telescope by the use of two convex lenses, which
is the form now most commonly adopted, and is a notable improvement
on Galilei’s instrument (chapter VI., § 118), one of the lenses of
which is concave; but Kepler does not seem himself to have had enough
mechanical skill to actually construct a telescope on this plan, or
to have had access to workmen capable of doing so for him; and it is
probable that Galilei’s enemy Scheiner (chapter VI., §§ 124, 125) was
the first person to use (about 1613) an instrument of this kind.
[Illustration: KEPLER.]
139. It has already been mentioned (chapter V., § 108) that when Tycho
was dividing the work of his observatory among his assistants he
assigned to Kepler the study of the planet Mars, probably as presenting
more difficulties than the subjects assigned to the others. It had been
known since the time of Coppernicus that the planets, including the
earth, revolved round the sun in paths that were at any rate not very
different from circles, and that the deviations from uniform circular
motion could be represented roughly by systems of eccentrics and
epicycles. The deviations from uniform circular motion were, however,
notably different in amount in different planets, being, for example,
very small in the case of Venus, relatively large in the case of Mars,
and larger still in that of Mercury. The _Prussian Tables_ calculated
by Reinhold on a Coppernican basis (chapter V., § 94) were soon found
to represent the actual motions very imperfectly, errors of 4° and 5°
having been noted by Tycho and Kepler, so that the principles on which
the tables were calculated were evidently at fault.
The solution of the problem was clearly more likely to be found by the
study of a planet in which the deviations from circular motion were as
great as possible. In the case of Mercury satisfactory observations
were scarce, whereas in the case of Mars there was an abundant series
recorded by Tycho, and hence it was true insight on Tycho’s part to
assign to his ablest assistant this particular planet, and on Kepler’s
to continue the research with unwearied patience. The particular system
of epicycles used by Coppernicus (chapter IV., § 87) having proved
defective, Kepler set to work to devise other geometrical schemes,
the results of which could be compared with observation. The places
of Mars as seen on the sky being a combined result of the motions
of Mars and of the earth in their respective orbits round the sun,
the irregularities of the two orbits were apparently inextricably
mixed up, and a great simplification was accordingly effected when
Kepler succeeded, by an ingenious combination of observations taken
at suitable times, in disentangling the irregularities due to the
earth from those due to the motion of Mars itself, and thus rendering
it possible to concentrate his attention on the latter. His fertile
imagination suggested hypothesis after hypothesis, combination after
combination of eccentric, epicycle, and equant; he calculated the
results of each and compared them rigorously with observation; and
at one stage he arrived at a geometrical scheme which was capable of
representing the observations with errors not exceeding 8′.[85] A man
of less intellectual honesty, or less convinced of the necessity of
subordinating theory to fact when the two conflict, might have rested
content with this degree of accuracy, or might have supposed Tycho’s
refractory observations to be in error. Kepler, however, thought
otherwise:—
“Since the divine goodness has given to us in Tycho Brahe a most
careful observer, from whose observations the error of 8′ is shewn
in this calculation, ... it is right that we should with gratitude
recognise and make use of this gift of God.... For if I could have
treated 8′ of longitude as negligible I should have already corrected
sufficiently the hypothesis ... discovered in chapter XVI. But as
they could not be neglected, these 8′ alone have led the way towards
the complete reformation of astronomy, and have been made the
subject-matter of a great part of this work.”[86]
140. He accordingly started afresh, and after trying a variety of
other combinations of circles decided that the path of Mars must
be an oval of some kind. At first he was inclined to believe in an
egg-shaped oval, larger at one end than at the other, but soon had to
abandon this idea. Finally he tried the simplest known oval curve,
the =ellipse=,[87] and found to his delight that it satisfied the
conditions of the problem, if the sun were taken to be at a focus of
the ellipse described by Mars.
It was further necessary to formulate the law of variation of the rate
of motion of the planet in different parts of its orbit. Here again
Kepler tried a number of hypotheses, in the course of which he fairly
lost his way in the intricacies of the mathematical questions involved,
but fortunately arrived, after a dubious process of compensation of
errors, at a simple law which agreed with observation. He found that
the planet moved fast when near the sun and slowly when distant from
it, in such a way that the area described or swept out in any time
by the line joining the sun to Mars was always proportional to the
time. Thus in fig. 60[88] the motion of Mars is most rapid at the
point A nearest to the focus S where the sun is, least rapid at A′,
and the shaded and unshaded portions of the figure represent equal
areas each corresponding to the motion of the planet during a month.
Kepler’s triumph at arriving at this result is expressed by the figure
of victory in the corner of the diagram (fig. 61) which was used in
establishing the last stage of his proof.
[Illustration: FIG. 60.—Kepler’s second law.]
141. Thus were established for the case of Mars the two important
results generally known as Kepler’s first two laws:—
1. _The planet describes an ellipse, the sun being in one focus._
2. _The straight line joining the planet to the sun sweeps out equal
areas in any two equal intervals of time._
The full history of this investigation, with the results already stated
and a number of developments and results of minor importance, together
with innumerable digressions and quaint comments on the progress of the
inquiry, was published in 1609 in a book of considerable length, the
_Commentaries on the Motions of Mars_.[89]
[Illustration: FIG. 61.—Diagram used by Kepler to establish his laws of
planetary motion. From the _Commentaries on Mars_.]
142. Although the two laws of planetary motion just given were only
fully established for the case of Mars, Kepler stated that the earth’s
path also must be an oval of some kind, and was evidently already
convinced—aided by his firm belief in the harmony of Nature—that
all the planets moved in accordance with the same laws. This view
is indicated in the dedication of the book to the Emperor Rudolph,
which gives a fanciful account of the work as a struggle against the
rebellious War-God Mars, as the result of which he is finally brought
captive to the feet of the Emperor and undertakes to live for the
future as a loyal subject. As, however, he has many relations in the
ethereal spaces—his father Jupiter, his grandfather Saturn, his dear
sister Venus, his faithful brother Mercury—and he yearns for them
and they for him _on account of the similarity of their habits_, he
entreats the Emperor to send out an expedition as soon as possible
to capture them also, and with that object to provide Kepler with the
“sinews of war” in order that he may equip a suitable army.
Although the money thus delicately asked for was only supplied very
irregularly, Kepler kept steadily in view the expedition for which it
was to be used, or, in plainer words, he worked steadily at the problem
of extending his elliptic theory to the other planets, and constructing
the tables of the planetary motions, based on Tycho’s observations, at
which he had so long been engaged.
143. In 1611 his patron Rudolph was forced to abdicate the imperial
crown in favour of his brother Matthias, who had little interest in
astronomy, or even in astrology; and as Kepler’s position was thus
rendered more insecure than ever, he opened negotiations with the
Estates of Upper Austria, as the result of which he was promised a
small salary, on condition of undertaking the somewhat varied duties
of teaching mathematics at the high school of Linz, the capital, of
constructing a new map of the province, and of completing his planetary
tables. For the present, however, he decided to stay with Rudolph.
In the same year Kepler lost his wife, who had long been in weak bodily
and mental health.
In the following year (1612) Rudolph died, and Kepler then moved
to Linz and took up his new duties there, though still holding the
appointment of mathematician to the Emperor and occasionally even
receiving some portion of the salary of the office. In 1613 he married
again, after a careful consideration, recorded in an extraordinary
but very characteristic letter to one of his friends, of the relative
merits of eleven ladies whom he regarded as possible; and the provision
of a proper supply of wine for his new household led to the publication
of a pamphlet, of some mathematical interest, dealing with the proper
way of measuring the contents of a cask with curved sides.[90]
144. In the years 1618-1621, although in some ways the most disturbed
years of his life, he published three books of importance—an _Epitome
of the Copernican Astronomy_, the _Harmony of the World_,[91] and a
treatise on _Comets_.
The second and most important of these, published in 1619, though the
leading idea in it was discovered early in 1618, was regarded by Kepler
as a development of his early _Mysterium Cosmographicum_ (§ 136). His
speculative and mystic temperament led him constantly to search for
relations between the various numerical quantities occurring in the
solar system; by a happy inspiration he thought of trying to get a
relation connecting the sizes of the orbits of the various planets
with their times of revolution round the sun, and after a number of
unsuccessful attempts discovered a simple and important relation,
commonly known as Kepler’s third law:—
_The squares of the times of revolution of any two planets (including
the earth) about the sun are proportional to the cubes of their mean
distances from the sun._
If, for example, we express the times of revolution of the various
planets in terms of any one, which may be conveniently taken to be that
of the earth, namely a year, and in the same way express the distances
in terms of the distance of the earth from the sun as a unit, then the
times of revolution of the several planets taken in the order Mercury,
Venus, Earth, Mars, Jupiter, Saturn are approximately ·24, ·615, 1,
1·88, 11·86, 29·457, and their distances from the sun are respectively
·387, ·723, 1, 1·524, 5·203, 9·539; if now we take the squares of
the first series of numbers (the square of a number being the number
multiplied by itself) and the cubes of the second series (the cube of
a number being the number multiplied by itself twice, or the square
multiplied again by the number), we get the two series of numbers given
approximately by the table:—
┌———————————┬——————————┬————————┬————————┬——————-┬——————————┬————————┐
│ │ Mercury. │ Venus. │ Earth. │ Mars. │ Jupiter. │ Saturn.│
├———————————┼——————————┼————————┼————————┼——————-┼——————————┼————————┤
│Square of }│ │ │ │ │ │ │
│ periodic }│ ·058 │ ·378 │ 1 │ 3·54 │ 140·7 │ 867·7 │
│ time }│ │ │ │ │ │ │
├———————————┼——————————┼————————┼————————┼——————-┼——————————┼————————┤
│Cube of }│ │ │ │ │ │ │
│ mean }│ ·058 │ ·378 │ 1 │ 3·54 │ 140·8 │ 867·9 │
│ distance }│ │ │ │ │ │ │
└———————————┴——————————┴————————┴————————┴——————-┴——————————┴————————┘
Here it will be seen that the two series of numbers, in the upper and
lower row respectively, agree completely for as many decimal places
as are given, except in the cases of the two outer planets, where the
lower numbers are slightly in excess of the upper. For this discrepancy
Newton afterwards assigned a reason (chapter IX., § 186), but with the
somewhat imperfect knowledge of the times of revolution and distances
which Kepler possessed the discrepancy was barely capable of detection,
and he was therefore justified—from his standpoint—in speaking of the
law as “precise.”[92]
[Illustration: FIG. 62.—The “music of the spheres,” according to
Kepler. From the _Harmony of the World_.]
It should be noticed further that Kepler’s law requires no knowledge of
the actual distances of the several planets from the sun, but only of
their relative distances, _i.e._ the number of times farther off from
the sun or nearer to the sun any planet is than any other. In other
words, it is necessary to have or to be able to construct a map of the
solar system correct in its _proportions_, but it is quite unnecessary
for this purpose to know the _scale_ of the map.
Although the _Harmony of the World_ is a large book, there is scarcely
anything of value in it except what has already been given. A good
deal of space is occupied with repetitions of the earlier speculations
contained in the _Mysterium Cosmographicum_, and most of the rest is
filled with worthless analogies between the proportions of the solar
system and the relations between various musical scales.
He is bold enough to write down in black and white the “music of the
spheres” (in the form shewn in fig. 62), while the nonsense which he
was capable of writing may be further illustrated by the remark which
occurs in the same part of the book: “The Earth sings the notes M I,
F A, M I, so that you may guess from them that in this abode of ours
MIsery (_miseria_) and FAmine (_fames_) prevail.”
145. The _Epitome of the Copernican Astronomy_, which appeared in
parts in 1618, 1620, and 1621, although there are no very striking
discoveries in it, is one of the most attractive of Kepler’s books,
being singularly free from the extravagances which usually render his
writings so tedious. It contains within moderately short compass, in
the form of question and answer, an account of astronomy as known at
the time, expounded from the Coppernican standpoint, and embodies
both Kepler’s own and Galilei’s latest discoveries. Such a textbook
supplied a decided want, and that this was recognised by enemies as
well as by friends was shewn by its prompt appearance in the Roman
_Index of Prohibited Books_ (cf. chapter VI., §§ 126, 132). The
_Epitome_ contains the first clear statement that the two fundamental
laws of planetary motion established for the case of Mars (§ 141)
were true also for the other planets (no satisfactory proof being,
however, given), and that they applied also to the motion of the moon
round the earth, though in this case there were further irregularities
which complicated matters. The theory of the moon is worked out in
considerable detail, both evection (chapter II., § 48) and variation
(chapter III., § 60; chapter V., § 111) being fully dealt with,
though the “annual equation” which Tycho had just begun to recognise
at the end of his life (chapter V., § 111) is not discussed. Another
interesting development of his own discoveries is the recognition that
his third law of planetary motion applied also to the movements of
the four satellites round Jupiter, as recorded by Galilei and Simon
Marius (chapter VI., § 118). Kepler also introduced in the _Epitome_ a
considerable improvement in the customary estimate of the distance of
the earth from the sun, from which those of the other planets could at
once be deduced.
If, as had been generally believed since the time of Hipparchus and
Ptolemy, the distance of the sun were 1,200 times the radius of the
earth, then the parallax (chapter II., §§ 43, 49) of the sun would
at times be as much as 3′, and that of Mars, which in some positions
is much nearer to the earth, proportionally larger. But Kepler had
been unable to detect any parallax of Mars, and therefore inferred
that the distances of Mars and of the sun must be greater than had
been supposed. Having no exact data to go on, he produced out of his
imagination and his ideas of the harmony of the solar system a distance
about three times as great as the traditional one. He argued that,
as the earth was the abode of measuring creatures, it was reasonable
to expect that the measurements of the solar system would bear some
simple relation to the dimensions of the earth. Accordingly he assumed
that the volume of the sun was as many times greater than the volume
of the earth as the distance of the sun was greater than the radius of
the earth, and from this quaint assumption deduced the value of the
distance already stated, which, though an improvement on the old value,
was still only about one-seventh of the true distance.
The _Epitome_ contains also a good account of eclipses both of the
sun and moon, with the causes, means of predicting them, etc. The
faint light (usually reddish) with which the face of the eclipsed moon
often shines is correctly explained as being sunlight which has passed
through the atmosphere of the earth, and has there been bent from a
straight course so as to reach the moon, which the light of the sun in
general is, owing to the interposition of the earth, unable to reach.
Kepler mentions also a ring of light seen round the eclipsed sun in
1567, when the eclipse was probably total, not annular (chapter II.,
§ 43), and ascribes it to some sort of luminous atmosphere round the
sun, referring to a description in Plutarch of the same appearance.
This seems to have been an early observation, and a rational though of
course very imperfect explanation, of that remarkable solar envelope
known as the =corona= which has attracted so much attention in the
last half-century (chapter XIII., § 301).
146. The treatise on _Comets_ (1619) contained an account of a comet
seen in 1607, afterwards famous as Halley’s comet (chapter X., §
200), and of three comets seen in 1618. Following Tycho, Kepler held
firmly the view that comets were celestial not terrestrial bodies, and
accounted for their appearance and disappearance by supposing that
they moved in straight lines, and therefore after having once passed
near the earth receded indefinitely into space; he does not appear to
have made any serious attempt to test this theory by comparison with
observation, being evidently of opinion that the path of a body which
would never reappear was not a suitable object for serious study.
He agreed with the observation made by Fracastor and Apian (chapter
III., § 69) that comets’ tails point away from the sun, and explained
this by the supposition that the tail is formed by rays of the sun
which penetrate the body of the comet and carry away with them some
portion of its substance, a theory which, allowance being made for the
change in our view’s as to the nature of light, is a curiously correct
anticipation of modern theories of comets’ tails (chapter XIII., § 304).
In a book intended to have a popular sale it was necessary to make
the most of the “meaning” of the appearance of a comet, and of its
influence on human affairs, and as Kepler was writing when the Thirty
Years’ War had just begun, while religious persecutions and wars
had been going on in Europe almost without interruption during his
lifetime, it was not difficult to find sensational events which had
happened soon after or shortly before the appearance of the comets
referred to. Kepler himself was evidently not inclined to attach much
importance to such coincidences; he thought that possibly actual
contact with a comet’s tail might produce pestilence, but beyond that
was not prepared to do more than endorse the pious if somewhat neutral
opinion that one of the uses of a comet is to remind us that we are
mortal. His belief that comets are very numerous is expressed in the
curious form: “There are as many arguments to prove the annual motion
of the earth round the sun as there are comets in the heavens.”
147. Meanwhile Kepler’s position at Linz had become more and more
uncomfortable, owing to the rising tide of the religious and political
disturbances which finally led to the outbreak of the Thirty Years’
War in 1618; but notwithstanding this he had refused in 1617 an offer
of a chair of mathematics at Bologna, partly through attachment to
his native country and partly through a well-founded distrust of the
Papal party in Italy. Three years afterwards he rejected also the
overtures made by the English ambassador, with a view to securing him
as an ornament to the court of James I., one of his chief grounds for
refusal in this case being a doubt whether he would not suffer from
being cooped up within the limits of an island. In 1619 the Emperor
Matthias died, and was succeeded by Ferdinand II., who as Archduke had
started the persecution of the Protestants at Gratz (§ 137) and who
had few scientific interests. Kepler was, however, after some delay,
confirmed in his appointment as Imperial Mathematician. In 1620 Linz
was occupied by the Imperialist troops, and by 1626 the oppression of
the Protestants by the Roman Catholics had gone so far that Kepler made
up his mind to leave, and, after sending his family to Regensburg, went
himself to Ulm.
148. At Ulm Kepler published his last great work. For more than a
quarter of a century he had been steadily working out in detail, on the
basis of Tycho’s observations and of his own theories, the motions of
the heavenly bodies, expressing the results in such convenient tabular
form that the determination of the place of any body at any required
time, as well as the investigation of other astronomical events such
as eclipses, became merely a matter of calculation according to fixed
rules; this great undertaking, in some sense the summing up of his own
and of Tycho’s work, was finally published in 1627 as the _Rudolphine
Tables_ (the name being given in honour of his former patron), and
remained for something like a century the standard astronomical tables.
It had long been Kepler’s intention, after finishing the tables,
to write a complete treatise on astronomy, to be called the _New
Almagest_; but this scheme was never fairly started, much less carried
out.
149. After a number of unsuccessful attempts to secure the arrears of
his salary, he was told to apply to Wallenstein, the famous Imperialist
general, then established in Silesia in a semi-independent position,
who was keenly interested in astrology and usually took about with
him one or more representatives of the art. Kepler accordingly joined
Wallenstein in 1628, and did astrology for him, in addition to
writing some minor astronomical and astrological treatises. In 1630
he travelled to Regensburg, where the Diet was then sitting, to press
in person his claims for various arrears of salary; but, worn out by
anxiety and by the fatigues of the journey, he was seized by a fever a
few days after his arrival, and died on November 15th (N.S.), 1630, in
his 59th year.
The inventory of his property, made after his death, shews that he was
in possession of a substantial amount, so that the effect of extreme
poverty which his letters convey must have been to a considerable
extent due to his over-anxious and excitable temperament.
150. In addition to the great discoveries already mentioned Kepler
made a good many minor contributions to astronomy, such as new
methods of finding the longitude, and various improvements in methods
of calculation required for astronomical problems. He also made
speculations of some interest as to possible causes underlying the
known celestial motions. Whereas the Ptolemaic system required a number
of motions round mere geometrical points, centres of epicycles or
eccentrics, equants, etc., unoccupied by any real body, and many such
motions were still required by Coppernicus, Kepler’s scheme of the
solar system placed a real body, the sun, at the most important point
connected with the path of each planet, and dealt similarly with the
moon’s motion round the earth and with that of the four satellites
round Jupiter. Motions of revolution came in fact to be associated
not with some central _point_ but with some central _body_, and it
became therefore an inquiry of interest to ascertain if there were
any connection between the motion and the central body. The property
possessed by a magnet of attracting a piece of iron at some little
distance from it suggested a possible analogy to Kepler, who had read
with care and was evidently impressed by the treatise _On the Magnet_
(De Magnete) published in 1600 by our countryman _William Gilbert_ of
Colchester (1540-1603). He suggested that the planets might thus be
regarded as connected with the sun, and therefore as sharing to some
extent the sun’s own motion of revolution. In other words, a certain
“carrying virtue” spread out from the sun, with or like the rays of
light and heat, and tried to carry the planets round with the sun.
“There is therefore a conflict between the carrying power of the sun
and the impotence or material sluggishness (_inertia_) of the planet;
each enjoys some measure of victory, for the former moves the planet
from its position and the latter frees the planet’s body to some
extent from the bonds in which it is thus held, ... but only to be
captured again by another portion of this rotatory virtue.”[93]
The annexed diagram is given by Kepler in illustration of this rather
confused and vague theory.
[Illustration: FIG. 63.—Kepler’s idea of gravity. From the _Epitome_.]
He believed also in a more general “gravity,” which he defined[94] as
“a mutual bodily affection between allied bodies tending towards their
union or junction,” and regarded the tides as due to an action of this
sort between the moon and the water of the earth. But the speculative
ideas thus thrown out, which it is possible to regard as anticipations
of Newton’s discovery of universal gravitation, were not in any way
developed logically, and Kepler’s mechanical ideas were too imperfect
for him to have made real progress in this direction.
151. There are few astronomers about whose merits such different
opinions have been held as about Kepler. There is, it is true, a
general agreement as to the great importance of his three laws of
planetary motion, and as to the substantial value of the _Rudolphine
Tables_ and of various minor discoveries. These results, however, fill
but a small part of Kepler’s voluminous writings, which are encumbered
with masses of wild speculation, of mystic and occult fancies, of
astrology, weather prophecies, and the like, which are not only
worthless from the standpoint of modern astronomy, but which—unlike
many erroneous or imperfect speculations—in no way pointed towards the
direction in which the science was next to make progress, and must
have appeared almost as unsound to sober-minded contemporaries like
Galilei as to us. Hence as one reads chapter after chapter without
a lucid still less a correct idea, it is impossible to refrain from
regrets that the intelligence of Kepler should have been so wasted,
and it is difficult not to suspect at times that some of the valuable
results which lie imbedded in this great mass of tedious speculation
were arrived at by a mere accident. On the other hand, it must not
be forgotten that such accidents have a habit of happening only to
great men, and that if Kepler loved to give reins to his imagination
he was equally impressed with the necessity of scrupulously comparing
speculative results with observed facts, and of surrendering without
demur the most beloved of his fancies if it was unable to stand this
test. If Kepler had burnt three-quarters of what he printed, we should
in all probability have formed a higher opinion of his intellectual
grasp and sobriety of judgment, but we should have lost to a great
extent the impression of extraordinary enthusiasm and industry, and of
almost unequalled intellectual honesty, which we now get from a study
of his works.