Pioneers of Science Part 4

Now was the time for the people whom Tycho had offended, for those who were jealous of his great fame and importance, as well as for those who cast longing eyes on his estate and endowments. The boy-king, too, unfortunately paid a visit to Tycho, and, venturing upon a decided opinion on some recondite subject, received a quiet setting down which he ill relished.

Letters written by Tycho about this time are full of foreboding. He greatly dreads having to leave Uraniburg, with which his whole life has for twenty years been bound up. He tries to comfort himself with the thought that, wherever he is sent, he will have the same heavens and the same stars over his head.

Gradually his Norwegian estate and his pension were taken away, and in five years poverty compelled him to abandon his magnificent temple, and to take a small house in Copenhagen.

Not content with this, Walchendorf got a Royal Commission appointed to inquire into the value of his astronomical labours. This sapient body reported that his work was not only useless, but noxious; and soon after he was attacked by the populace in the public street.

Nothing was left for him now but to leave the country, and he went into Germany, leaving his wife and instruments to follow him whenever he could find a home for them.

His wanderings in this dark time--some two years--are not quite clear; but at last the enlightened Emperor of Bohemia, Rudolph II., invited him to settle in Prague. Thither he repaired, a castle was given him as an observatory, a house in the city, and 3000 crowns a year for life. So his instruments were set up once more, students flocked to hear him and to receive work at his hands--among them a poor youth, John Kepler, to whom he was very kind, and who became, as you know, a still greater man than his master.

But the spirit of Tycho was broken, and though some good work was done at Prague--more observations made, and the Rudolphine tables begun--yet the hand of death was upon him. A painful disease seized him, attended with sleeplessness and temporary delirium, during the paroxysms of which he frequently exclaimed, _Ne frustra vixisse videar_. ("Oh that it may not appear that I have lived in vain!")

Quietly, however, at last, and surrounded by his friends and relatives, this fierce, pa.s.sionate soul pa.s.sed away, on the 24th of October, 1601.

His beloved instruments, which were almost a part of himself, were stored by Rudolph in a museum with scrupulous care, until the taking of Prague by the Elector Palatine's troops. In this disturbed time they got smashed, dispersed, and converted to other purposes. One thing only was saved--the great bra.s.s globe, which some thirty years after was recognized by a later king of Denmark as having belonged to Tycho, and deposited in the Library of the Academy of Sciences at Copenhagen, where I believe it is to this day.

The island of Huen was overrun by the Danish n.o.bility, and nothing now remains of Uraniburg but a mound of earth and two pits.

As to the real work of Tycho, that has become immortal enough,--chiefly through the labours of his friend and scholar whose life we shall consider in the next lecture.

SUMMARY OF FACTS FOR LECTURE III

_Life and work of Kepler._ Kepler was born in December, 1571, at Weil in Wurtemberg. Father an officer in the duke's army, mother something of a virago, both very poor. Kepler was utilized as a tavern pot-boy, but ultimately sent to a charity school, and thence to the University of Tubingen. Health extremely delicate; he was liable to violent attacks all his life. Studied mathematics, and accepted an astronomical lectureship at Graz as the first post which offered. Endeavoured to discover some connection between the number of the planets, their times of revolution, and their distances from the sun. Ultimately hit upon his fanciful regular-solid hypothesis, and published his first book in 1597.

In 1599 was invited by Tycho to Prague, and there appointed Imperial mathematician, at a handsome but seldom paid salary. Observed the new star of 1604. Endeavoured to find the law of refraction of light from Vitellio's measurements, but failed. a.n.a.lyzed Tycho's observations to find the true law of motion of Mars. After incredible labour, through innumerable wrong guesses, and six years of almost incessant calculation, he at length emerged in his two "laws"--discoveries which swept away all epicycles, deferents, equants, and other remnants of the Greek system, and ushered in the dawn of modern astronomy.

LAW I. _Planets move in ellipses, with the Sun in one focus._

LAW II. _The radius vector (or line joining sun and planet) sweeps out equal areas in equal times._

Published his second book containing these laws in 1609. Death of Rudolph in 1612, and subsequent increased misery and misfortune of Kepler. Ultimately discovered the connection between the times and distances of the planets for which he had been groping all his mature life, and announced it in 1618:--

LAW III. _The square of the time of revolution (or year) of each planet is proportional to the cube of its mean distance from the sun._

The book in which this law was published ("On Celestial Harmonies") was dedicated to James of England. In 1620 had to intervene to protect his mother from being tortured for witchcraft. Accepted a professorship at Linz. Published the Rudolphine tables in 1627, embodying Tycho's observations and his own theory. Made a last effort to overcome his poverty by getting the arrears of his salary paid at Prague, but was unsuccessful, and, contracting brain fever on the journey, died in November, 1630, aged 59.

A man of keen imagination, indomitable perseverance, and uncompromising love of truth, Kepler overcame ill-health, poverty, and misfortune, and placed himself in the very highest rank of scientific men. His laws, so extraordinarily discovered, introduced order and simplicity into what else would have been a chaos of detailed observations; and they served as a secure basis for the splendid erection made on them by Newton.

_Seven planets of the Ptolemaic system--_ Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn.

_Six planets of the Copernican system--_ Mercury, Venus, Earth, Mars, Jupiter, Saturn.

_The five regular solids, in appropriate order--_ Octahedron, Icosahedron, Dodecahedron, Tetrahedron, Cube.

_Table ill.u.s.trating Kepler's third law._

+---------+---------------+-----------+---------------+----------------+ | | Mean distance | Length | Cube of the | Square of the | | Planet. | from Sun. | of Year. | Distance. | Time. | | | D | T | D^3 | T^2 | +---------+---------------+-----------+---------------+----------------+ | Mercury | 3871 | 24084 | 05801 | 05801 | | Venus | 7233 | 61519 | 37845 | 37846 | | Earth | 10000 | 10000 | 10000 | 10000 | | Mars | 15237 | 18808 | 35375 | 35375 | | Jupiter | 52028 | 11862 | 14083 | 14070 | | Saturn | 95388 | 29457 | 86792 | 86770 | +---------+---------------+-----------+---------------+----------------+

The length of the earth's year is 365256 days; its mean distance from the sun, taken above as unity, is 92,000,000 miles.

LECTURE III

KEPLER AND THE LAWS OF PLANETARY MOTION

It is difficult to imagine a stronger contrast between two men engaged in the same branch of science than exists between Tycho Brahe, the subject of last lecture, and Kepler, our subject on the present occasion.

The one, rich, n.o.ble, vigorous, pa.s.sionate, strong in mechanical ingenuity and experimental skill, but not above the average in theoretical and mathematical power.

The other, poor, sickly, devoid of experimental gifts, and unfitted by nature for accurate observation, but strong almost beyond compet.i.tion in speculative subtlety and innate mathematical perception.

The one is the complement of the other; and from the fact of their following each other so closely arose the most surprising benefits to science.

The outward life of Kepler is to a large extent a mere record of poverty and misfortune. I shall only sketch in its broad features, so that we may have more time to attend to his work.

He was born (so his biographer a.s.sures us) in longitude 29 7', lat.i.tude 48 54', on the 21st of December, 1571. His parents seem to have been of fair condition, but by reason, it is said, of his becoming surety for a friend, the father lost all his slender income, and was reduced to keeping a tavern. Young John Kepler was thereupon taken from school, and employed as pot-boy between the ages of nine and twelve. He was a sickly lad, subject to violent illnesses from the cradle, so that his life was frequently despaired of. Ultimately he was sent to a monastic school and thence to the University of Tubingen, where he graduated second on the list. Meanwhile home affairs had gone to rack and ruin.

His father abandoned the home, and later died abroad. The mother quarrelled with all her relations, including her son John; who was therefore glad to get away as soon as possible.

All his connection with astronomy up to this time had been the hearing the Copernican theory expounded in University lectures, and defending it in a college debating society.

An astronomical lectureship at Graz happening to offer itself, he was urged to take it, and agreed to do so, though stipulating that it should not debar him from some more brilliant profession when there was a chance.

For astronomy in those days seems to have ranked as a minor science, like mineralogy or meteorology now. It had little of the special dignity with which the labours of Kepler himself were destined so greatly to aid in endowing it.

Well, he speedily became a thorough Copernican, and as he had a most singularly restless and inquisitive mind, full of appreciation of everything relating to number and magnitude--was a born speculator and thinker just as Mozart was a born musician, or Bidder a born calculator--he was agitated by questions such as these: Why are there exactly six planets? Is there any connection between their orbital distances, or between their orbits and the times of describing them?

These things tormented him, and he thought about them day and night. It is characteristic of the spirit of the times--this questioning why there should be six planets. Nowadays, we should simply record the fact and look out for a seventh. Then, some occult property of the number six was groped for, such as that it was equal to 1 + 2 + 3 and likewise equal to 1 2 3, and so on. Many fine reasons had been given for the seven planets of the Ptolemaic system (see, for instance, p. 106), but for the six planets of the Copernican system the reasons were not so cogent.

Again, with respect to their successive distances from the sun, some law would seem to regulate their distance, but it was not known.

(Parenthetically I may remark that it is not known even now: a crude empirical statement known as Bode's law--see page 294--is all that has been discovered.)

Once more, the further the planet the slower it moved; there seemed to be some law connecting speed and distance. This also Kepler made continual attempts to discover.

[Ill.u.s.tration: FIG. 26.--Orbits of some of the planets drawn to scale: showing the gap between Mars and Jupiter.]

One of his ideas concerning the law of the successive distances was based on the inscription of a triangle in a circle. If you inscribe in a circle a large number of equilateral triangles, they envelop another circle bearing a definite ratio to the first: these might do for the orbits of two planets (see Fig. 27). Then try inscribing and circ.u.mscribing squares, hexagons, and other figures, and see if the circles thus defined would correspond to the several planetary orbits.

But they would not give any satisfactory result. Brooding over this disappointment, the idea of trying solid figures suddenly strikes him.

"What have plane figures to do with the celestial orbits?" he cries out; "inscribe the regular solids." And then--brilliant idea--he remembers that there are but five. Euclid had shown that there could be only five regular solids.[4] The number evidently corresponds to the gaps between the six planets. The reason of there being only six seems to be attained. This coincidence a.s.sures him he is on the right track, and with great enthusiasm and hope he "represents the earth's...o...b..t by a sphere as the norm and measure of all"; round it he circ.u.mscribes a dodecahedron, and puts another sphere round that, which is approximately the orbit of Mars; round that, again, a tetrahedron, the corners of which mark the sphere of the orbit of Jupiter; round that sphere, again, he places a cube, which roughly gives the orbit of Saturn.

[Ill.u.s.tration: FIG. 27.--Many-sided polygon or approximate circle enveloped by straight lines, as for instance by a number of equilateral triangles.]

On the other hand, he inscribes in the sphere of the earth's...o...b..t an icosahedron; and inside the sphere determined by that, an octahedron; which figures he takes to inclose the spheres of Venus and of Mercury respectively.