CHAPTER XIX.

_Character of Galileo—Miscellaneous details—his

Death—Conclusion._

THE remaining years of Galileo's life were spent at Arcetri, where

indeed, even if the Inquisition had granted his liberty, his increasing

age and infirmities would probably have detained him. The rigid caution

with which he had been watched in Florence was in great measure relaxed,

and he was permitted to see the friends who crowded round him to express

their respect and sympathy. The Grand Duke visited him frequently, and

many distinguished strangers, such as Gassendi and Deodati, came into

Italy solely for the purpose of testifying their admiration of his

character. Among other visitors the name of Milton will be read with

interest: we may probably refer to the effects of this interview the

allusions to Galileo's discoveries, so frequently introduced into his

poem. Milton mentions in his 'Areopagitica,' that he saw Galileo whilst

in Italy, but enters into no details of his visit.

Galileo was fond of society, and his cheerful and popular manners

rendered him an universal favourite among those who were admitted to his

intimacy. Among these, Viviani, who formed one of his family during the

three last years of his life, deserves particular notice, on account of

the strong attachment and almost filial veneration with which he ever

regarded his master and benefactor. His long life, which was prolonged

to the completion of his 81st year in 1703, enabled him to see the

triumphant establishment of the truths on account of which Galileo had

endured so many insults; and even in his old age, when in his turn he

had acquired a claim to the reverence of a younger generation, our Royal

Society, who invited him among them in 1696, felt that the complimentary

language in which they addressed him as the first mathematician of the

age would have been incomplete and unsatisfactory without an allusion to

the friendship that gained him the cherished title of "The last pupil of

Galileo."[170]

Torricelli, another of Galileo's most celebrated followers, became a

member of his family in October, 1641: he first learned mathematics from

Castelli, and occasionally lectured for him at Rome, in which manner he

was employed when Galileo, who had seen his book 'On Motion,' and

augured the greatest success from such a beginning, invited him to his

house—an offer which Torricelli eagerly embraced, although he enjoyed

the advantages of it but for a short time. He afterwards succeeded

Galileo in his situation at the court of Florence,[171] but survived him

only a few years.

It is from the accounts of Viviani and Gherardini that we principally

draw the following particulars of Galileo's person and character:—Signor

Galileo was of a cheerful and pleasant countenance, especially in his

old age, square built, and well proportioned in stature, and rather

above the middle size. His complexion was fair and sanguine, his eyes

brilliant, and his hair of a reddish cast. His constitution was

naturally strong, but worn out by fatigue of mind and body, so as

frequently to be reduced to a state of the utmost weakness. He was

subject to attacks of hypochondria, and often molested by severe and

dangerous illnesses, occasioned in great measure by his sleepless

nights, the whole of which he frequently spent in astronomical

observations. During upwards of forty-eight years of his life, he was

tormented with acute rheumatic pains, suffering particularly on any

change of weather. He found himself most free from these pains whilst

residing in the country, of which consequently he became very fond:

besides, he used to say that in the country he had greater freedom to

read the book of Nature, which lay there open before him. His library

was very small, but well chosen, and open to the use of the friends whom

he loved to see assembled round him, and whom he was accustomed to

receive in the most hospitable manner. He ate sparingly himself; but was

particularly choice in the selection of his wines, which in the latter

part of his life were regularly supplied out of the Grand Duke's

cellars. This taste gave an additional stimulus to his agricultural

pursuits, and many of his leisure hours were spent in the cultivation

and superintendence of his vineyards. It should seem that he was

considered a good judge of wine; for Viviani has preserved one of his

receipts in a collection of miscellaneous experiments. In it he strongly

recommends that for wine of the first quality, that juice only should be

employed, which is pressed out by the mere weight of the heaped grapes,

which would probably be that of the ripest fruit. The following letter,

written in his 74th year, is dated, "From my prison at Arcetri.—I am

forced to avail myself of your assistance and favour, agreeably to your

obliging offers, in consequence of the excessive chill of the weather,

and of old age, and from having drained out my grand stock of a hundred

bottles, which I laid in two years ago; not to mention some minor

particulars during the last two months, which I received from my Serene

Master, the Most Eminent Lord Cardinal, their Highnesses the Princes,

and the Most Excellent Duke of Guise, besides cleaning out two barrels

of the wine of this country. Now, I beg that with all due diligence and

industry, and with consideration, and taking counsel with the most

refined palates, you will provide me with two cases, that is to say,

with forty flasks of different wines, the most exquisite that you can

find: take no thought of the expense, because I stint myself so much in

all other pleasures that I can afford to lay out something at the

request of Bacchus, without giving offence to his two companions Ceres

and Venus. You must be careful to leave out neither Scillo nor Carino (I

believe they meant to call them Scylla and Charybdis), nor the country

of my master, Archimedes of Syracuse, nor Greek wines, nor clarets, &c.

&c. The expense I shall easily be able to satisfy, but not the infinite

obligation."

In his expenditure Galileo observed a just mean between avarice and

profusion: he spared no cost necessary for the success of his many and

various experiments, and spent large sums in charity and hospitality,

and in assisting those in whom he discovered excellence in any art or

profession, many of whom he maintained in his own house. His temper was

easily ruffled, but still more easily pacified. He seldom conversed on

mathematical or philosophical topics except among his intimate friends;

and when such subjects were abruptly brought before him, as was often

the case by the numberless visitors he was in the habit of receiving, he

showed great readiness in turning the conversation into more popular

channels, in such manner however that he often contrived to introduce

something to satisfy the curiosity of the inquirers. His memory was

uncommonly tenacious, and stored with a vast variety of old songs and

stories, which he was in the constant habit of quoting and alluding to.

His favourite Italian authors were Ariosto, Petrarca, and Berni, great

part of whose poems he was able to repeat. His excessive admiration of

Ariosto determined the side which he took against Tasso in the virulent

and unnecessary controversy which has divided Italy so long on the

respective merits of these two great poets; and he was accustomed to say

that reading Tasso after Ariosto was like tasting cucumbers after

melons. When quite a youth, he wrote a great number of critical remarks

on Tasso's Gerusalemme Liberata, which one of his friends borrowed, and

forgot to return. For a long time it was thought that the manuscript had

perished, till the Abbé Serassi discovered it, whilst collecting

materials for his Life of Tasso, published at Rome in 1785. Serassi

being a violent partizan of Tasso, but also unwilling to lose the credit

of the discovery, copied the manuscript, but without any intention of

publishing it, "till he could find leisure for replying properly to the

sophistical and unfounded attacks of a critic so celebrated on other

accounts." He announced his discovery as having been made "in one of the

famous libraries at Rome," which vague indication he with some reason

considered insufficient to lead to a second discovery. On Serassi's

death his copy was found, containing a reference to the situation of the

original; the criticisms were published, and form the greatest part of

the last volume of the Milan edition of Galileo's works. The manuscript

was imperfect at the time of this second discovery, several leaves

having been torn out, it is not known by whom.

The opinion of the most judicious Italian critics appears to be, that it

would have been more for Galileo's credit if these remarks had never

been made public: they are written in a spirit of flippant violence,

such as might not be extraordinary in a common juvenile critic, but

which it is painful to notice from the pen of Galileo. Two or three

sonnets are extant written by Galileo himself, and in two instances he

has not scrupled to appropriate the conceits of the poet he affected to

undervalue.[172] It should be mentioned that Galileo's matured taste

rather receded from the violence of his early prejudices, for at a later

period of his life he used to shun comparing the two; and when forced to

give an opinion he said, "that Tasso's appeared the finer poem, but that

Ariosto gave him the greater pleasure." Besides these sonnets, there is

extant a short burlesque poem written by him, "In abuse of Gowns," when,

on his first becoming Professor at Pisa, he found himself obliged by

custom to wear his professional habit in every company. It is written

not without humour, but does not bear comparison with Berni, whom he

imitated.

There are several detached subjects treated of by Galileo, which may be

noticed in this place. A letter by him containing the solution of a

problem in Chances is probably the earliest notice extant of the

application of mathematics to that interesting subject: the

correspondence between Pascal and Fermat, with which its history is

generally made to begin, not having taken place till at least twelve

years later. There can be little doubt after the clear account of Carlo

Dati, that Galileo was the first to examine the curve called the

Cycloid, described by a point in the rim of a wheel rolling on a

straight line, which he recommended as a graceful form for the arch of a

bridge at Pisa. He even divined that the area contained between it and

its base is exactly three times that of the generating circle. He seems

to have been unable to verify this guess by strict geometrical

reasoning, for Viviani tells an odd story, that in order to satisfy his

doubts he cut out several large cycloids of pasteboard, but finding the

weight in every trial to be rather less than three times that of the

circle, he suspected the proportion to be irrational, and that there was

some error in his estimation; the inquiry he abandoned was afterwards

resumed with success by his pupil Torricelli.[173]

The account which Lagalla gives of an experiment shown in his presence

by Galileo, carries the observation of the phosphorescence of the

Bologna stone at least as far back as 1612.[174] Other writers mention

the name of an alchymist, who according to them discovered it

accidentally in 1603. Cesi, Lagalla, and one or two others, had passed

the night at Galileo's house, with the intention of observing Venus and

Saturn; but, the night being cloudy, the conversation turned on other

matters, and especially on the nature of light, "on which Galileo took a

small wooden box at daybreak before sunrise, and showed us some small

stones in it, desiring us to observe that they were not in the least

degree luminous. Having then exposed them for some time to the twilight,

he shut the window again; and in the midst of the dark room showed us

the stones, shining and glistening with a faint light, which we saw

presently decay and become extinguished." In 1640, Liceti attempted to

refer the effect of the earthshine upon the moon to a similar

phosphorescent quality of that luminary, to which Galileo, then aged 76,

replied by a long and able letter, enforcing the true explanation he had

formerly given.

Although quite blind, and nearly deaf, the intellectual powers of

Galileo remained to the end of his life; but he occasionally felt that

he was overworking himself, and used to complain to his friend Micanzio

that he found his head too busy for his body. "I cannot keep my restless

brain from grinding on, although with great loss of time; for whatever

idea comes into my head with respect to any novelty, drives out of it

whatever I had been thinking of just before." He was busily engaged in

considering the nature of the force of percussion, and Torricelli was

employed in arranging his investigations for a continuation of the

'Dialogues on Motion,' when he was seized with an attack of fever and

palpitation of the heart, which, after an illness of two months, put an

end to his long, laborious, and useful life, on the 8th of January,

1642, just one year before his great successor Newton was born.

The malice of his enemies was scarcely allayed by his death. His right

of making a will was disputed, as having died a prisoner to the

Inquisition, as well as his right to burial in consecrated ground. These

were at last conceded, but Urban anxiously interfered to prevent the

design of erecting a monument to him in the church of Santa Croce, in

Florence, for which a large sum had been subscribed. His body was

accordingly buried in an obscure corner of the church, which for upwards

of thirty years after his death was unmarked even by an inscription to

his memory. It was not till a century later that the splendid monument

was erected which now covers his and Viviani's remains. When their

bodies were disinterred in 1737 for the purpose of being removed to

their new resting-place, Capponi, the president of the Florentine

Academy, in a spirit of spurious admiration, mutilated Galileo's body,

by removing the thumb and forefinger of the right-hand, and one of the

vertebræ of the back, which are still preserved in some of the Italian

museums. The monument was put up at the expense of his biographer,

Nelli, to whom Viviani's property descended, charged with the condition

of erecting it. Nor was this the only public testimony which Viviani

gave of his attachment. The medal which he struck in honour of Galileo

has already been mentioned; he also, as soon as it was safe to do so,

covered every side of the house in which he lived with laudatory

inscriptions to the same effect. A bust of Galileo was placed over the

door, and two bas-reliefs on each side representing some of his

principal discoveries. Not less than five other medals were struck in

honour of him during his residence at Padua and Florence, which are all

engraved in Venturi's Memoirs.

There are several good portraits of Galileo extant, two of which, by

Titi and Subtermanns, are engraved in Nelli's Life of Galileo. Another

by Subtermanns is in the Florentine Gallery, and an engraving from a

copy of this is given by Venturi. There is also a very fine engraving

from the original picture. An engraving from another original picture is

in the frontispiece of the Padua edition of his works. Salusbury seems

in the following passage to describe a portrait of Galileo painted by

himself: "He did not contemn the other inferior arts, for he had a good

hand in sculpture and carving; but his particular care was to paint

well. By the pencil he described what his telescope discovered; in one

he exceeded art, in the other, nature. Osorius, the eloquent bishop of

Sylva, esteems one piece of Mendoza the wise Spanish minister's

felicity, to have been this, that he was contemporary to Titian, and

that by his hand he was drawn in a fair tablet. And Galilæus, lest he

should want the same good fortune, made so great a progress in this

curious art, that he became his own _Buonarota_; and because there was

no other copy worthy of his pencil, drew himself." No other author makes

the slightest allusion to such a painting; and it appears more likely

that Salusbury should be mistaken than that so interesting a portrait

should have been entirely lost sight of.

Galileo's house at Arcetri was standing in 1821, when Venturi visited

it, and found it in the same state in which Galileo might be supposed to

have left it. It is situated nearly a mile from Florence, on the

south-eastern side, and about a gun-shot to the north-west of the

convent of St. Matthew. Nelli placed a suitable inscription over the

door of the house, which belonged in 1821 to a Signor Alimari.[175]

Although Nelli's Life of Galileo disappointed the expectations that had

been formed of it, it is impossible for any admirer of Galileo not to

feel the greatest degree of gratitude towards him, for the successful

activity with which he rescued so many records of the illustrious

philosopher from destruction. After Galileo's death, the principal part

of his books, manuscripts, and instruments, were put into the charge of

Viviani, who was himself at that time an object of great suspicion; most

of them he thought it prudent to conceal, till the superstitious

outcries against Galileo should be silenced. At Viviani's death, he left

his library, containing a very complete collection of the works of all

the mathematicians who had preceded him (and amongst them those of

Galileo, Torricelli, and Castelli, all which were enriched with notes

and additions by himself), to the hospital of St. Mary at Florence,

where an extensive library already existed. The directors of the

hospital sold this unique collection in 1781, when it became entirely

dispersed. The manuscripts in Viviani's possession passed to his nephew,

the Abbé Panzanini, together with the portraits of the chief personages

of the Galilean school, Galileo's instruments, and, among other

curiosities, the emerald ring which he wore as a member of the Lyncean

Academy. A great number of these books and manuscripts were purchased at

different times by Nelli, after the death of Panzanini, from his

relations, who were ignorant or regardless of their value. One of his

chief acquisitions was made by an extraordinary accident, related by

Tozzetti with the following details, which we repeat, as they seem to

authenticate the story:—"In the spring of 1739, the famous Doctor Lami

went out according to his custom to breakfast with some of his friends

at the inn of the Bridge, by the starting-place; and as he and Sig.

Nelli were passing through the market, it occurred to them to buy some

Bologna sausages from the pork-butcher, Cioci, who was supposed to excel

in making them. They went into the shop, had their sausages cut off and

rolled in paper, which Nelli put into his hat. On reaching the inn, and

calling for a plate to put them in, Nelli observed that the paper in

which they had been rolled was one of Galileo's letters. He cleaned it

as well as he could with his napkin, and put it into his pocket without

saying a word to Lami; and as soon as he returned into the city, and

could get clear of him, he flew to the shop of Cioci, who told him that

a servant whom he did not know brought him from time to time similar

letters, which he bought by weight as waste paper. Nelli bought all that

remained, and on the servant's next reappearance in a few days, he

learned the quarter whence they came, and after some time succeeded at a

small expense in getting into his own possession an old corn-chest,

containing all that still remained of the precious treasures which

Viviani had concealed in it ninety years before."[176]

The earliest biographical notice of Galileo is that in the Obituary of

the Mercurio Italico, published at Venice in 1647, by Vittorio Siri. It

is very short, but contains an exact enumeration of his principal works

and discoveries. Rossi, who wrote under the name of Janus Nicius

Erythræus, introduced an account of Galileo in his Pinacotheca Imaginum

Illustrium, in which the story of his illegitimacy first made its

appearance. In 1664, Salusbury published a life of Galileo in the second

volume of his Mathematical Collections, the greater part of which is a

translation of Galileo's principal works. Almost the whole edition of

the second volume of Salusbury's book was burnt in the great fire of

London. Chauffepié says that only one copy is known to be extant in

England: this is now in the well-known library of the Earl of

Macclesfield, to whose kindness the author is much indebted for the use

he has been allowed to make of this unique volume. A fragment of this

second volume is in the Bodleian Library at Oxford. The translations in

the preceding pages are mostly founded upon Salusbury's version.

Salusbury's account, although that of an enthusiastic admirer of

Galileo, is too prolix to be interesting: the general style of the

performance may be guessed from the title of the first chapter—'Of Man

in general, and how he excelleth all the other Animals.' After informing

his readers that Galileo was born at Pisa, he proceeds:—"Italy is

affirmed to have been the first that peopled the world after the

universal deluge, being governed by Janus, Cameses, and Saturn, &c." His

description of Galileo's childhood is somewhat quaint. "Before others

had left making of dirt pyes, he was framing of diagrams; and whilst

others were whipping of toppes, he was considering the cause of their

motion." It is on the whole tolerably correct, especially if we take

into account that Salusbury had not yet seen Viviani's Life, though

composed some years earlier.

The Life of Galileo by Viviani was first written as an outline of an

intended larger work, but this latter was never completed. This sketch

was published in the Memoirs of the Florentine Academy, of which Galileo

had been one of the annual presidents, and afterwards prefixed to the

complete editions of Galileo's works; it is written in a very agreeable

and flowing style, and has been the groundwork of most subsequent

accounts. Another original memoir by Niccolò Gherardini, was published

by Tozzetti. A great number of references to authors who have treated of

Galileo is given by Sach in his Onomasticon. An approved Latin memoir by

Brenna is in the first volume of Fabroni's Vitæ Italorum Illustrium; he

has however fallen into several errors: this same work contains the

lives of several of his principal followers.

The article in Chauffepié's Continuation of Bayle's Dictionary does not

contain anything which is not in the earlier accounts.

Andrès wrote an essay entitled 'Saggio sulla Filosofia del Galileo,'

published at Mantua 1776; and Jagemann published his 'Geschichte des

Leben des Galileo' at Leipzig, in 1787;[177] neither of these the author

has been able to meet with. An analysis of the latter may be seen in

Kästner's 'Geschichte der Mathematik, Göttingen, 1800,' from which it

does not appear to contain any additional details. The 'Elogio del

Galileo' by Paolo Frisi, first published at Leghorn in 1775, is, as its

title expresses, rather in the nature of a panegyric than of a

continuous biographical account. It is written with very great elegance

and intimate knowledge of the subjects of which it treats. Nelli gave

several curious particulars with respect to Galileo in his 'Saggio di

Storia Letteraria Fiorentina, Lucca, 1759;' and in 1793 published his

large work entitled 'Vita e Commercio Letterario di Galileo Galilei.' So

uninteresting a book was probably never written from such excellent

materials. Two thick quarto volumes are filled with repetitions of the

accounts that were already in print, the bulky preparation of which

compelled the author to forego the publication of the vast collection of

original documents which his unwearied zeal and industry had collected.

This defect has been in great measure supplied by Venturi in 1818 and

1821, who has not only incorporated in his work many of Nelli's

manuscripts, but has brought together a number of scattered notices of

Galileo and his writings from a variety of outlying sources—a service

which the writer is able to appreciate from having gone through the

greatest part of the same labour before he was fortunate enough to meet

with Venturi's book. Still there are many letters cited by Nelli, which

do not appear either in his book or Venturi's. Carlo Dati, in 1663,

quotes "the registers of Galileo's correspondence arranged in

alphabetical order, in ten large volumes."[178] The writer has no means

of ascertaining what collection this may have been; it is difficult to

suppose that one so arranged should have been lost sight of. It is

understood that a life of Galileo is preparing at this moment in

Florence, by desire of the present Grand Duke, which will probably throw

much additional light on the character and merits of this great and

useful philosopher.

The first editions of his various treatises, as mentioned by Nelli, are

given below. Clement, in his 'Bibliothèque Curieuse,' has pointed out

such among them, and the many others which have been printed, as have

become rare.

The Florentine edition is the one used by the Academia della Crusca for

their references; for which reason its paging is marked in the margin of

the edition of Padua, which is much more complete, and is the one which

has been on the present occasion principally consulted.

The latter contains the Dialogue on the System, which was not suffered

to be printed in the former editions. The twelve first volumes of the

last edition of Milan are a mere transcript of that of Padua: the

thirteenth contains in addition the Letter to the Grand Duchess, the

Commentary on Tasso, with some minor pieces. A complete edition is still

wanted, embodying all the recently discovered documents, and omitting

the verbose commentaries, which, however useful when they were written,

now convey little information that cannot be more agreeably and more

profitably learned in treatises of a later date.

Such was the life, and such were the pursuits, of this extraordinary

man. The numberless inventions of his acute industry; the use of the

telescope, and the brilliant discoveries to which it led; the patient

investigation of the laws of weight and motion; must all be looked upon

as forming but a part of his real merits, as merely particular

demonstrations of the spirit in which he everywhere withstood the

despotism of ignorance, and appealed boldly from traditional opinions to

the judgments of reason and common sense. He claimed and bequeathed to

us the right of exercising our faculties in examining the beautiful

creation which surrounds us. Idolized by his friends, he deserved their

affection by numberless acts of kindness; by his good humour, his

affability, and by the benevolent generosity with which he devoted

himself and a great part of his limited income to advance their talents

and fortunes. If an intense desire of being useful is everywhere worthy

of honour; if its value is immeasurably increased, when united to genius

of the highest order; if we feel for one who, notwithstanding such

titles to regard, is harassed by cruel persecution,—then none deserve

our sympathy, our admiration, and our gratitude, more than Galileo.

_List of Galileo's Works._

Le Operazioni del Compasso Geom. e Milit.

Padova, 1606.

Fol. Difesa di Gal. Galilei contr. all. cal. et impost. di Bald. Capra

Venezza, 1607. 4to.

Sydereus Nuncius Venetiis, 1610. 4to.

Discorso int. alle cose che stanno in su l'Acqua

Firenze, 1612. 4to.

Novantiqua SS. PP. Doctrina de S. Scripturæ Testimoniis

Argent, 1612. 4to.

Istoria e Demostr. int. alle Macchie Solari

Roma, 1613. 4to.

Risp. alle oppos. del S. Lod. delle Colombe e del S. Vinc. di Grazia

Firenze, 1615. 4to.

Discorso delle Comete di Mario Guiducci

Firenze, 1619. 4to.

Dialogo sopra i due Massimi Sistemi del Mondo

Firenze, 1632. 4to.

Discorso e Demostr. intorno alle due nuove Scienze

Leida, 1638. 4to.

Della Scienza Meccanica Ravenna, 1649. 4to.

Trattato della Sfera Roma, 1655. 4to.

Discorso sopra il Flusso e Reflusso. (Scienze Fisiche di Tozzetti.)

Firenze, 1780. 4to.

Considerazioni sul Tasso Roma, 1793.

Trattato della Fortificazione. (Memorie di Venturi.)

Modena, 1818. 4to.

The editions of his collected works (in which is contained much that was

never published separately) are—

Opere di Gal. Galilei, Linc. Nob. Fior. &c.

Bologna, 1656. 2 vols. 4to.

Opere di Gal. Galilei, Nob. Fior. Accad. Linc. &c.

Firenze, 1718. 3 vols. 4to.

Opere di Gal. Galilei Padova, 1744. 4 vols. 4to.

Opere di Gal. Galilei Milano, 1811. 13 vols. 8vo.

CORRECTIONS.

_Page Co. Line._

5 1 2,

_Add_: His instructor was the celebrated botanist, Andreas

Cæsalpinus, who was professor of medicine at Pisa from 1567 to 1592.

Hist. Acad. Pisan.; Pisis, 1791.

8 2 18,

_Add_: According to Kästner, his German name was Wursteisen.

8 2 21, _for_ 1588 _read_ 1586.

15 1 57, _for_ 1632 _read_ 1630.

17 1 29,

Salusbury alludes to the instrument described and figured in "The

Use of the Sector, Crosse Staffe, and other Instruments. London,

1624." It is exactly Galileo's Compass.

17 1 52, _for_ Burg, a German, _read_ Burgi, a Swiss.

27 2 17,

The author here called Brutti was an Englishman: his real name,

perhaps, was Bruce. See p. 99.

50 1 14,

Kepler's Epitome was not published till 1619: it was then inserted

in the Index.

73 1 60, _for_ under _read_ turned from.

80 2 44, _for_ any _read_ an indefinitely small.

FOOTNOTES:

[170] The words of his diploma are: Galilæi in mathematicis disciplinis

discipulus, in ærumnis socius, Italicum ingenium ita perpolivit optimis

artibus ut inter mathematicos sæculi nostri facile princeps per orbem

litterarium numeretur.—Tiraboschi.

[171] On this occasion the taste of the time showed itself in the

following anagram:—

Evangelista Torricellieus,

En virescit Galilæus alter.

[172] Compare Son. ii. v. 8 & 9; and Son. iii. v. 2 & 3, with Ger. Lib.

c. iv. st. 76, and c. vii. st. 19.—The author gladly owns his

obligation for these remarks to the kindness of Sig. Panizzi, Professor

of Italian in the University of London.

[173] Lettera di Timauro Antiate. Firenze, 1663.

[174] De phænomenis in orbe Lunæ. Venetiis, 1612.

[175] Venturi.

[176] Notizie sul Ingrandimento delle Scienze Fisiche. Firenze, 1780.

[177] Venturi.

[178] Lettera di Timauro Antiate.

LIFE OF KEPLER.

CHAPTER I.

_Introduction—Birth and Education of Kepler—He is appointed

Astronomical Professor at Gratz—Publishes the 'Mysterium

Cosmographicum.'_

IN the account of the life and discoveries of Galileo, we have

endeavoured to inculcate the safety and fruitfulness of the method

followed by that great reformer in his search after physical truth. As

his success furnishes the best instance of the value of the inductive

process, so the failures and blunders of his adversaries supply equally

good examples of the dangers and the barrenness of the opposite course.

The history of JOHN KEPLER might, at the first view, suggest conclusions

somewhat inconsistent with this remark. Every one who is but moderately

acquainted with astronomy is familiar with the discoveries which that

science owes to him; the manner in which he made them is, perhaps, not

so generally known. This extraordinary man pursued, almost invariably,

the hypothetical method. His life was passed in speculating on the

results of a few principles assumed by him, from very precarious

analogies, as the causes of the phenomena actually observed in Nature.

We nevertheless find that he did, in spite of this unphilosophical

method, arrive at discoveries which have served as guides to some of the

most valuable truths of modern science.

The difficulty will disappear if we attend more closely to the details

of Kepler's investigations. We shall perceive that to an unusual degree

of rashness in the formation of his systems, he added a quality very

rarely possessed by philosophers of the hypothetical school. One of the

greatest intellectual vices of the latter was a wilful blindness to the

discrepancy of facts from their creed, a perverse and obstinate

resistance to physical evidence, leading not unfrequently to an attempt

at disguising the truth. From this besetting sin of the school, which

from an intellectual fault often degenerated into a moral one, Kepler

was absolutely free. Scheme after scheme, resting originally upon little

beyond his own glowing imagination, but examined and endeared by the

ceaseless labour of years, was unhesitatingly sacrificed, as soon as its

insufficiency became indisputable, to make room for others as little

deserving support. The history of philosophy affords no more remarkable

instance of sincere uncompromising love of truth. To this virtue he owed

his great discoveries: it must be attributed to his unhappy method that

he made no more.

In considering this opinion upon the real nature of Kepler's title to

fame, it ought not to be forgotten that he has exposed himself at a

disadvantage on which certainly very few philosophers would venture. His

singular candour allowed him to comment upon his own errors with the

same freedom as if scrutinizing the work of a stranger; careless whether

the impression on his readers were favourable or otherwise to himself,

provided it was instructive. Few writers have spoken so much, and so

freely of themselves, as Kepler. He records, on almost every occasion,

the train of thought by which he was led to each of the discoveries that

eventually repaid his perseverance; and he has thus given us a most

curious and interesting view of the workings of a mind of great, though

eccentric power. "In what follows," says he (when introducing a long

string of suppositions, of which he had already discovered the fallacy),

"let the reader pardon my credulity, whilst working out all these

matters by my own ingenuity. For it is my opinion that the occasions by

which men have acquired a knowledge of celestial phenomena are not less

admirable than the discoveries themselves." Agreeing altogether with

this opinion in its widest application, we have not scrupled, in the

following sketch, to introduce at some length an account even of

Kepler's erroneous speculations; they are in themselves very amusing,

and will have the additional utility of proving the dangerous tendency

of his method; they will show by how many absurd theories, and how many

years of wasted labour, his real discoveries and services to science lie

surrounded.

JOHN KEPLER was born (as we are assured by his earliest biographer

Hantsch) in long. 29° 7´, lat. 48° 54´, on the 21st day of December,

1571. On this spot stands the imperial city of Weil, in the duchy of

Wirtemberg. His parents were Henry Kepler and Catherine Guldenmann, both

of noble, though decayed families. Henry Kepler, at the time of his

marriage, was a petty officer in the Duke of Wirtemberg's service; and a

few years after the birth of his eldest son John, he joined the army

then serving in the Netherlands. His wife followed him, leaving their

son, then in his fifth year, at Leonberg, under the care of his

grandfather. He was a seven months child, very weak and sickly; and

after recovering with difficulty from a severe attack of small-pox, he

was sent to school in 1577. Henry Kepler's limited income was still

farther reduced on his return into Germany, the following year, in

consequence of the absconding of one of his acquaintance, for whom he

had incautiously become surety. His circumstances were so much narrowed

by this misfortune, that he was obliged to sell his house, and nearly

all that he possessed, and for several years he supported his family by

keeping a tavern at Elmendingen. This occasioned great interruption to

young Kepler's education; he was taken from school, and employed in

menial services till his twelfth year, when he was again placed in the

school at Elmendingen. In the following year he was again seized with a

violent illness, so that his life was almost despaired of. In 1586, he

was admitted into the monastic school of Maulbronn, where the cost of

his education was defrayed by the Duke of Wirtemberg. This school was

one of those established on the suppression of the monasteries at the

Reformation, and the usual course of education followed there required

that the students, after remaining a year in the superior classes,

should offer themselves for examination at the college of Tubingen for

the degree of bachelor: they then returned to their school with the

title of veterans; and after completing the studies taught there, they

were admitted as resident students at Tubingen, proceeded in about a

year to the degree of master, and were then allowed to commence their

course of theology. The three years of Kepler's life following his

admission to Maulbronn, were marked by periodical returns of several of

the disorders which had well nigh proved fatal to him in his childhood.

During the same time disagreements arose between his parents, in

consequence of which his father quitted his home, and soon after died

abroad. After his father's departure, his mother also quarrelled with

her relations, having been treated, says Hantsch, "with a degree of

barbarity by her husband and brother-in-law that was hardly exceeded

even by her own perverseness:" one of his brothers died, and the

family-affairs were in the greatest confusion. Notwithstanding these

disadvantages, Kepler took his degree of master in August 1591,

attaining the second place in the annual examination. The first name on

the list was John Hippolytus Brentius.

Whilst he was thus engaged at Tubingen, the astronomical lectureship at

Gratz, the chief town of Styria, became vacant by the death of George

Stadt, and the situation was offered to Kepler. Of this first occasion

of turning his thoughts towards astronomy, he has himself given the

following account: "As soon as I was of an age to feel the charms of

philosophy, I embraced every part of it with intense desire, but paid no

especial regard to astronomy. I had indeed capacity enough for it, and

learned without difficulty the geometrical and astronomical theorems

occurring in the usual course of the school, being well grounded in

figures, numbers, and proportions. But those were compulsory

studies—there was nothing to show a particular turn for astronomy. I

was educated at the expense of the Duke of Wirtemberg, and when I saw

such of my companions as the duke selected to send abroad shrink in

various ways from their employments, out of fondness for home, I, who

was more callous, had early made up my mind to go with the utmost

readiness whithersoever I might be sent. The first offering itself was

an astronomical post, which I was in fact forced to accept by the

authority of my tutors; not that I was alarmed, in the manner I had

condemned in others, by the remoteness of the situation, but by the

unexpected and contemptible nature of the office, and by the slightness

of my information in this branch of philosophy. I entered on it,

therefore, better furnished with talent than knowledge: with many

protestations that I was not abandoning my claim to be provided for in

some other more brilliant profession. What progress I made in the first

two years of my studies, may be seen in my 'Mysterium Cosmographicum;'

and the encouragement given me by my tutor, Mästlin, to take up the

science of astronomy, may be read in the same book, and in his letter

which is prefixed to the 'Narrative of Rheticus.' I looked on that

discovery as of the highest importance, and still more so, because I saw

how greatly it was approved by Mästlin."

The nature of the singular work to which Kepler thus refers with so much

complacency, will be best shown by quoting some of the most remarkable

parts of it, and especially the preface, in which he briefly details

some of the theories he successively examined and rejected, before

detecting (as he imagined he had here done) the true cause of the number

and order of the heavenly bodies. The other branches of philosophy with

which he occupied himself in his younger years, were those treated by

Scaliger in his 'Exoteric Exercises,' to the study of which book Kepler

attributed the formation of many of his opinions; and he tells us that

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 tide, the shape of the continents,

and inland seas, and things of this sort." He also says, that by his

first success with the heavens, his hopes were greatly inflamed of

discovering similar analogies in the rest of the visible world, and for

this reason, named his book merely a Prodromus, or Forerunner, meaning,

at some future period, to subjoin the Aftercomer, or Sequel. But this

intention was never fulfilled; either his imagination failed him, or,

what is more likely, the laborious calculations in which his

astronomical theories engaged him, left him little time for turning his

attention to objects unconnected with his first pursuit.

It is seldom that we are admitted to trace the progress of thought in

those who have distinguished themselves by talent and originality; and

although the whole of the following speculations begin and end in error,

yet they are so characteristic, and exhibit such an extraordinary

picture of the extravagances into which Kepler's lively imagination was

continually hurrying him, that we cannot refrain from citing nearly the

whole preface. From it, better than from any enumeration of

peculiarities, the reader will at once apprehend the nature of his

disposition.

"When I was attending the celebrated Mästlin, six years ago, at

Tubingen, I was disturbed by the manifold inconveniences of the common

theory of the universe, and so delighted with Copernicus, whom Mästlin

was frequently in the habit of quoting with great respect, that I not

only often defended his propositions in the physical disputations of the

candidates, but also wrote a correct essay on the primary motion,

maintaining, that it is caused by the rotation of the earth. And I was

then at that point that I attributed to the earth the motion of the sun

on physical (or, if you will, on metaphysical) grounds, as Copernicus

had done for mathematical reasons. And, by this practice, I came by

degrees, partly from Mästlin's instructions, and partly from my own

efforts, to understand the superior mathematical convenience of the

system of Copernicus beyond Ptolemy's. This labour might have been

spared me, by Joachim Rheticus, who has shortly and clearly explained

everything in his first Narrative. While incidentally engaged in these

labours, in the intermission of my theology, it happened conveniently

that I succeeded George Stadt in his situation at Gratz, where the

nature of my office connected me more closely with these studies.

Everything I had learned from Mästlin, or had acquired of myself, was

there of great service to me in explaining the first elements of

astronomy. And, as in Virgil, '_Fama mobilitate viget, viresque acquirit

eundo_,' so it was with me, that the diligent thought on these things

was the occasion of still further thinking: until, at last, in the year

1595, when I had some intermission of my lectures allowed me, I brooded

with the whole energy of my mind on this subject. There were three

things in particular, of which I pertinaciously sought the causes why

they are not other than they are: the number, the size, and the motion

of the orbits. I attempted the thing at first with numbers, and

considered whether one of the orbits might be double, triple, quadruple,

or any other multiple of the others, and how much, according to

Copernicus, each differed from the rest. I spent a great deal of time in

that labour, as if it were mere sport, but could find no equality either

in the proportions or the differences, and I gained nothing from this

beyond imprinting deeply in my memory the distances as assigned by

Copernicus; unless, perhaps, reader, this record of my various attempts

may force your assent, backwards and forwards, as the waves of the sea;

until tired at length, you will willingly repose yourself, as in a safe

haven, on the reasons explained in this book. However, I was comforted

in some degree, and my hopes of success were supported as well by other

reasons which will follow presently, as by observing that the motions in

every case seemed to be connected with the distances, and that where

there was a great gap between the orbits, there was the same between the

motions. And I reasoned, that if God had adapted motions to the orbits

in some relation to the distances, it was probable that he had also

arrayed the distances themselves in relation to something else.

"Finding no success by this method, I tried another, of singular

audacity. I inserted a new planet between Mars and Jupiter, and another

between Venus and Mercury, both of which I supposed invisible, perhaps

on account of their smallness, and I attributed to each a certain period

of revolution.[179] I thought that I could thus contrive some equality

of proportions, increasing between every two, from the sun to the fixed

stars. For instance, the Earth is nearer Venus in parts of the

terrestrial orbit, than Mars is to the Earth in parts of the orbit of

Mars. But not even the interposition of a new planet sufficed for the

enormous gap between Mars and Jupiter; for the proportion of Jupiter to

the new planet was still greater than that of Saturn to Jupiter. And

although, by this supposition, I got some sort of a proportion, yet

there was no reasonable conclusion, no certain determination of the

number of the planets either towards the fixed stars, till we should get

as far as them, nor ever towards the Sun, because the division in this

proportion of the residuary space within Mercury might be continued

without end. Nor could I form any conjecture, from the mobility of

particular numbers, why, among an infinite number, so few should be

moveable. The opinion advanced by Rheticus in his Narrative is

improbable, where he reasons from the sanctity of the number six to the

number of the six moveable heavens; for he who is inquiring of the frame

of the world itself, must not derive reasons from these numbers, which

have gained importance from things of later date.

"I sought again, in another way, whether the distance of every planet is

not as the residuum of a sine; and its motion as the residuum of the

sine of the complement in the same quadrant.

[Illustration]

"Conceive the square AB to be constructed, whose side AC is equal to the

semidiameter of the universe. From the angle B opposite to A the place

of the sun, or centre of the world, describe the quadrant DC with the

radius BC. Then in AC, the true radius of the world, let the sun, fixed

stars, and planets be marked at their respective distances, and from

these points draw lines parallel to BC, meeting the quadrant. I imagined

the moving force acting on each of the planets to be in the proportion

of these parallels. In the line of the sun is infinity, because AD is

touched, and not cut, by the quadrant: therefore the moving force is

infinite in the sun, as deriving no motion except from its own act. In

Mercury the infinite line is cut off at K, and therefore at this point

the motion is comparable with the others. In the fixed stars the line is

altogether lost, and compressed into a mere point C; therefore at that

point there is no moving force. This was the theorem, which was to be

tried by calculation; but if any one will reflect that two things were

wanting to me, first, that I did not know the size of the _Sinus Totus_,

that is, the radius of the proposed quadrant; secondly, that the

energies of the motions were not thus expressed otherwise than in

relation one to another; whoever, I say, well considers this, will

doubt, not without reason, as to the progress I was likely to make in

this difficult course. And yet, with unremitting labour, and an infinite

reciprocation of sines and arcs, I did get so far as to be convinced

that this theory could not hold.

"Almost the whole summer was lost in these annoying labours; at last, by

a trifling accident, I lighted more nearly on the truth. I looked on it

as an interposition of Providence, that I should obtain by chance, what

I had failed to discover with my utmost exertions; and I believed this

the more, because I prayed constantly that I might succeed, if

Copernicus had really spoken the truth. It happened on the 9th or

19th[180] day of July, in the year 1595, that, having occasion to show,

in my lecture-room, the passages of the great conjunctions through eight

signs, and how they pass gradually from one trine aspect to another, I

inscribed in a circle a great number of triangles, or quasi-triangles,

so that the end of one was made the beginning of another. In this manner

a smaller circle was shadowed out by the points in which the lines

crossed each other.

[Illustration: A Scheme of the great Conjunctions of SATURN & JUPITER,

their leaps through eight Signs, and their passages through all the four

Triplicities of the Zodiac.]

"The radius of a circle inscribed in a triangle is half the radius of

that described about it; therefore the proportion between these two

circles struck the eye as almost identical with that between Saturn and

Jupiter, and the triangle is the first figure, just as Saturn and

Jupiter are the first planets. On the spot I tried the second distance

between Jupiter and Mars with a square, the third with a pentagon, the

fourth with a hexagon. And as the eye again cried out against the second

distance between Jupiter and Mars, I combined the square with a triangle

and a pentagon. There would be no end of mentioning every trial. The

failure of this fruitless attempt was the beginning of the last

fortunate one; for I reflected, that in this way I should never reach

the sun, if I wished to observe the same rule throughout; nor should I

have any reason why there were six, rather than twenty or a hundred

moveable orbits. And yet figures pleased me, as being quantities, and as

having existed before the heavens; for quantity was created with matter,

and the heavens afterwards. But if (this was the current of my

thoughts), in relation to the quantity and proportion of the six orbits,

as Copernicus has determined them among the infinite other figures, five

only could be found having peculiar properties above the rest, my

business would be done. And then again it struck me, what have plane

figures to do among solid orbits? Solid bodies ought rather to be

introduced. This, reader, is the invention and the whole substance of

this little work; for if any one, though but moderately skilled in

geometry, should hear these words hinted, the five regular solids will

directly occur to him with the proportions of their circumscribed and

inscribed spheres: he has immediately before his eyes that scholium of

Euclid to the 18th proposition of his 13th Book, in which it is proved

to be impossible that there should be, or be imagined, more than five

regular bodies.

"What is worthy of admiration (since I had then no proof of any

prerogatives of the bodies with regard to their order) is, that

employing a conjecture which was far from being subtle, derived from the

distances of the planets, I should at once attain my end so happily in

arranging them, that I was not able to change anything afterwards with

the utmost exercise of my reasoning powers. In memory of the event, I

write down here for you the sentence, just as it fell from me, and in

the words in which it was that moment conceived:—The Earth is the

circle, the measurer of all; round it describe a dodecahedron, the

circle including this will be Mars. Round Mars describe a tetrahedron,

the circle including this will be Jupiter. Describe a cube round

Jupiter, the circle including this will be Saturn. Now, inscribe in the

Earth an icosahedron, the circle inscribed in it will be Venus. Inscribe

an octahedron in Venus, the circle inscribed in it will be Mercury. This

is the reason of the number of the planets.

[Illustration]

"This was the cause, and such the success, of my labour: now read my

propositions in this book. The intense pleasure I have received from

this discovery never can be told in words. I regretted no more the time

wasted; I tired of no labour; I shunned no toll of reckoning; days and

nights I spent in calculations; until I could see whether this opinion

would agree with the orbits of Copernicus, or whether my joy was to

vanish into air. I willingly subjoin that sentiment of Archytas, as

given by Cicero: 'If I could mount up into heaven, and thoroughly

perceive the nature of the world, and beauty of the stars, that

admiration would be without a charm for me, unless I had some one like

you, reader, candid, attentive, and eager for knowledge, to whom to

describe it.' If you acknowledge this feeling, and are candid, you will

refrain from blame, such as not without cause I anticipate; but if,

leaving that to itself, you fear lest these things be not ascertained,

and that I have shouted triumph before victory, at least approach these

pages, and learn the matter in consideration: you will not find, as just

now, new and unknown planets interposed; that boldness of mine is not

approved, but those old ones very little loosened, and so furnished by

the interposition (however absurd you may think it) of rectilinear

figures, that in future you may give a reason to the rustics when they

ask for the hooks which keep the skies from falling.—Farewell."

In the third chapter Kepler mentions, that a thickness must be allowed

to each orb sufficient to include the greatest and least distance of

the planet from the sun. The form and result of his comparison with the

real distances are as follows:—

Book V.

If the {Saturn } be taken {Jupiter = 577} {635 Ch. 9

inner {Jupiter} at 1000 {Mars = 333} According to {333—14

Surface {Mars } then the {Earth = 795} Copernicus {757—19

of the {Earth } outer {Venus = 795} they are {794—21, 22

orbit of {Venus } one of {Mercury = 577} {723—27

It will be observed, that Kepler's results were far from being entirely

satisfactory; but he seems to have flattered himself, that the

differences might be attributed to erroneous measurements. Indeed, the

science of observation was then so much in its infancy, that such an

assertion might be made without incurring much risk of decisive

refutation.

Kepler next endeavoured to determine why the regular solids followed in

this rather than any other order; and his imagination soon created a

variety of essential distinctions between the cube, pyramid, and

dodecahedron, belonging to the superior planets, and the other two.

The next question examined in the book, is the reason why the zodiac is

divided into 360 degrees; and on this subject, he soon becomes enveloped

in a variety of subtle considerations, (not very intelligible in the

original, and still more difficult to explain shortly to others

unacquainted with it,) in relation to the divisions of the musical

scale; the origin of which he identifies with his five favourite solids.

The twentieth chapter is appropriated to a more interesting inquiry,

containing the first traces of his finally successful researches into

the proportion between the distances of the planets, and the times of

their motions round the sun. He begins with the generally admitted fact,

that the more distant planets move more slowly; but in order to show

that the proportion, whatever it may be, is not the simple one of the

distances, he exhibits the following little Table:—

♄

+--+--------+

| |D. Scr. | ♃

+--+--------+---------+

|♄ |10759.12| D. Scr. | ♂

+--+--------+---------+--------+

|♃ | 6159 | 4332.37 |D. Scr. | ♁

+--+--------+---------+--------+-------+

|♂ | 1785 | 1282 | 686.59 |D. Scr.| ♀

+--+--------+---------+--------+-------+-------+

|♁ | 1174 | 843 | 452 |365.15 |D. Scr.| ☿

+--+--------+---------+--------+-------+-------+---------+

|♀ | 844 | 606 | 325 |262.30 |224.42 | D. Scr. |

+--+--------+---------+--------+-------+-------+---------+

|☿ | 434 | 312 | 167 |135 |115 | 87.58 |

At the head of each vertical column is placed the real time (in days and

sexagesimal parts) of the revolution of the planet placed above it, and

underneath the days due to the other inferior planets, if they observed

the proportion of distance. Hence it appears that this proportion in

every case gives a time greater than the truth; as for instance, if the

earth's rate of revolution were to Jupiter's in the proportion of their

distances, the second column shows that the time of her period would be

843 instead of 365¼ days; so of the rest. His next attempt was to

compare them by two by two, in which he found that he arrived at a

proportion something like the proportion of the distances, although as

yet far from obtaining it exactly. This process amounts to taking the

quotients obtained by dividing the period of each planet by the period

of the one next beyond.

{ ♄ 10759.27} be successively taken to { ♃ 403

{ ♃ 4332.37 } consist of 1000 equal { ♂ 159

{ ♂ 686.59 } parts, the planet next { ♁ 532

For if each of the { ♁ 365.15 } below will contain { ♀ 615

periods of { ♀ 244.42 } of those parts in { ☿ 392

But if the distance of each planet in { ♃ 572

succession be taken to consist of { ♂ 290

1000 equal parts, the distance of { ♁ 658

the next below will contain, according { ♀ 719

to Copernicus, in { ☿ 500

From this table he argued that to make the proportions agree, we must

assume one of two things, "either that the moving intelligences of the

planets are weakest in those which 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."

We stop here to insert a note added by Kepler to the later editions, and

shall take advantage of the same interruption to warn the reader not to

confound this notion of Kepler with the theory of a gravitating force

towards the Sun, in the sense in which we now use those words. According

to our theory, the effect of the presence of the Sun upon the planet is

to pull it towards the centre in a straight line, and the effect of the

motion thus produced combined with the motion of the planet, which if

undisturbed would be in a straight line inclined to the direction of the

radius, is, that it describes a curve round the Sun. Kepler considered

his planets as perfectly quiet and unwilling to move when left alone;

and that this virtue supposed by him to proceed in every direction out

of the Sun, swept them round, just as the sails of a windmill would

carry round anything which became entangled in them. In other parts of

his works Kepler mentions having speculated on a real attractive force

in the centre; but as he knew that the planets are not always at the

same distance from the Sun, and conceived erroneously, that to remove

them from their least to their greatest distance a repulsive force must

be supposed alternating with an attractive one, he laid aside this

notion as improbable. In a note he acknowledges that when he wrote the

passage just quoted, imbued as he then was with Scaliger's notions on

moving intelligences, he literally believed "that each planet was moved

by a living spirit, but afterwards came to look on the moving cause as a

corporeal though immaterial substance, something in the nature of light

which is observed to diminish similarly at increased distances." He then

proceeds as follows in the original text.

"Let us then assume, as is very probable, that motion is dispensed by

the sun in the same manner as light. The proportion in which light

emanating from a centre is diminished, is taught by optical writers: for

there is the same quantity of light, or of the solar rays, in the small

circles as in the large; and therefore, as it is more condensed in the

former, more attenuated in the latter, a measure of the attenuation may

be derived from the proportion of the circles themselves, both in the

case of light and of the moving virtue. Therefore, by how much the orbit

of Venus is greater than that of Mercury, in the same proportion will

the motion of the latter be stronger, or more hurried, or more swift, or

more powerful, or by whatever other word you like to express the fact,

than that of the former. But a larger orbit would require a

proportionably longer time of revolution, even though the moving force

were the same. Hence it follows that the one cause of a greater distance

of the planet from the Sun, produces a double effect in increasing the

period, and conversely the increase of the periods will be double the

difference of the distances. Therefore, half the increment added to the

shorter period ought to give the true proportion of the distances, so

that the sum should represent the distance of the superior planet, on

the same scale on which the shorter period represents the distance of

the interior one. For instance, the period of Mercury is nearly 88 days;

that of Venus is 224⅔, the difference is 136⅔: half of this is 68⅓,

which, added to 88, gives 156⅓. The mean distance of Venus ought,

therefore, to be, in proportion to that of Mercury, as 156⅓ to 88. If

this be done with all the planets, we get the following results, taking

successively, as before, the distance of each planet at 1000.

The distance in parts of which } ♃ 574 But according { 572

the distance of the next } ♂ 274 to Copernicus { 290

superior planet contains 1000, } ♁ 694 they are { 658

is at } ♀ 762 respectively { 719

} ☿ 563 { 500

As you see, we have now got nearer the truth."

Finding that this theory of the rate of diminution would not bring him

quite close to the result he desired to find, Kepler immediately

imagined another. This latter occasioned him a great deal of perplexity,

and affords another of the frequently recurring instances of the waste

of time and ingenuity occasioned by his impetuous and precipitate

temperament. Assuming the distance of any planet, as for instance of

Mars, to be the unit of space, and the virtue at that distance to be the

unit of force, he supposed that as many particles as the virtue at the

Earth gained upon that of Mars, so many particles of distance did the

Earth lose. He endeavoured to determine the respective positions of the

planets upon this theory, by the rules of false position, but was much

astonished at finding the same exactly as on his former hypothesis. The

fact was, as he himself discovered, although not until after several

years, that he had become confused in his calculation; and when half

through the process, had retraced his steps so as of course to arrive

again at the numbers from which he started, and which he had taken from

his former results. This was the real secret of the identity of the two

methods; and if, when he had taken the distance of Mars at 1000, instead

of assuming the distance of the earth at 694, as he did, he had taken

any other number, and operated upon it in the same manner, he would

have had the same reason for relying on the accuracy of his supposition.

As it was, the result utterly confounded him; and he was obliged to

leave it with the remark, that "the two theories are thus proved to be

the same in fact, and only different in form; although how that can

possibly be, I have never to this day been able to understand."—His

perplexity was very reasonable; they are by no means the same; it was

only his method of juggling with the figures which seemed to connect

them.

Notwithstanding all its faults, the genius and unwearied perseverance

displayed by Kepler in this book, immediately ranked him among

astronomers of the first class; and he received the most flattering

encomiums from many of the most celebrated; among others, from Galileo

and Tycho Brahe, whose opinion he invited upon his performance. Galileo

contented himself with praising in general terms the ingenuity and good

faith which appeared so conspicuously in it. Tycho Brahe entered into a

more detailed criticism of the work, and, as Kepler shrewdly remarked,

showed how highly he thought of it by advising him to try to adapt

something of the same kind to the Tychonic system. Kepler also sent a

copy of his book to the imperial astronomer, Raimar, with a

complimentary letter, in which he exalted him above all other

astronomers of the age. Raimar had surreptitiously acquired a notion of

Tycho Brahe's theory, and published it as his own; and Tycho, in his

letter, complained of Kepler's extravagant flattery. This drew a long

apologetical reply from Kepler, in which he attributed the admiration he

had expressed of Raimar to his own want of information at that time,

having since met with many things in Euclid and Regiomontanus, which he

then believed original in Raimar. With this explanation, Tycho professed

himself perfectly satisfied.

FOOTNOTES:

[179] The following scrupulous note added by Kepler in 1621 to a

subsequent edition of this work, deserves to be quoted. It shows how

entirely superior he was to the paltriness of attempting to appropriate

the discoveries of others, of which many of his contemporaries had

exhibited instances even on slighter pretences than this passage might

have afforded him. The note is as follows: "Not circulating round

Jupiter like the Medicæan stars. Be not deceived. I never had them in my

thoughts, but, like the other primary planets, including the sun in the

centre of the system within their orbits."

[180] This inconvenient mode of dating was necessary before the new or

Gregorian style was universally adopted.

CHAPTER II.

_Kepler's Marriage—He joins Tycho Brahe at Prague—Is appointed

Imperial Mathematician—Treatise on the New Star._

THE publication of this extraordinary book, early as it occurs in the

history of Kepler's life, was yet preceded by his marriage. He had

contemplated this step so early as 1592; but that suit having been

broken off, he paid his addresses, in 1596, to Barbara Muller von

Muhleckh. This lady was already a widow for the second time, although

two years younger than Kepler himself. On occasion of this alliance he

was required to prove the nobility of his family, and the delay

consequent upon the inquiry postponed the marriage till the following

year. He soon became involved in difficulties in consequence of this

inconsiderate engagement: his wife's fortune was less than he had been

led to expect, and he became embroiled on that account with her

relations. Still more serious inconvenience resulted to him from the

troubled state in which the province of Styria was at that time, arising

out of the disputes in Bohemia and the two great religious parties into

which the empire was now divided, the one headed by Rodolph, the feeble

minded emperor,—the other by Matthias, his ambitious and enterprising

brother.

In the year following his marriage, he thought it prudent, on account of

some opinions he had unadvisedly promulgated, (of what nature does not

very distinctly appear,) to withdraw himself from Gratz into Hungary.

Thence he transmitted several short treatises to his friend Zehentmaier,

at Tubingen—"On the Magnet," "On the Cause of the Obliquity of the

Ecliptic," and "On the Divine Wisdom, as shown in the Creation." Little

is known of these works beyond the notice taken of them in Zehentmaier's

answers. Kepler has himself told us, that his magnetic philosophy was

built upon the investigations of Gilbert, of whom he always justly spoke

with the greatest respect.

About the same time a more violent persecution had driven Tycho Brahe

from his observatory of Uraniburg, in the little island of Hueen, at the

entrance of the Baltic. This had been bestowed on him by the munificence

of Frederick I. of Denmark, who liberally furnished him with every means

of prosecuting his astronomical observations. After Frederick's death,

Tycho found himself unable to withstand the party which had constantly

opposed him, and was forced, at a great loss and much inconvenience, to

quit his favourite island. On the invitation of the emperor, Rudolph

II., he then betook himself, after a short stay at Hamburg, to the

castle of Benach, near Prague, which was assigned to him with an annual

pension of three thousand florins, a truly munificent provision in those

times and that country.

Kepler had been eager to see Tycho Brahe since the latter had intimated

that his observations had led him to a more accurate determination of

the excentricities of the orbits of the planets. By help of this, Kepler

hoped that his theory might be made to accord more nearly with the

truth; and on learning that Tycho was in Bohemia, he immediately set out

to visit him, and arrived at Prague in January, 1600. From thence he

wrote a second letter to Tycho, not having received the answer to his

former apology, again excusing himself for the part he had appeared to

take with Raimar against him. Tycho replied immediately in the kindest

manner, and begged he would repair to him directly:—"Come not as a

stranger, but as a very welcome friend; come and share in my

observations with such instruments as I have with me, and as a dearly

beloved associate." During his stay of three or four months at Benach,

it was settled that Tycho should apply to the emperor, to procure him

the situation of assistant in the observatory. Kepler then returned to

Gratz, having previously received an intimation, that he might do so in

safety. The plan, as it had been arranged between them was, that a

letter should be procured from the emperor to the states of Styria,

requesting that Kepler might join Tycho Brahe for two years, and retain

his salary during that time: a hundred florins were to be added annually

by the emperor, on account of the greater dearness of living at Prague.

But before everything was concluded, Kepler finally threw up his

situation at Gratz, in consequence of new dissensions. Fearing that this

would utterly put an end to his hopes of connecting himself with Tycho,

he determined to revive his claims on the patronage of the Duke of

Wirtemberg. With this view he entered into correspondence with Mästlin

and some of his other friends at Tubingen, intending to prosecute his

medical studies, and offer himself for the professorship of medicine in

that university. He was dissuaded from this scheme by the pressing

instances of Tycho, who undertook to exert himself in procuring a

permanent settlement for him from the emperor, and assured him, even if

that attempt should fail, that the language he had used when formerly

inviting him to visit him at Hamburg, should not be forgotten. In

consequence of this encouragement, Kepler abandoned his former scheme,

and travelled again with his wife to Prague. He was detained a long time

on the road by violent illness, and his money became entirely exhausted.

On this he wrote complainingly to Tycho, that he was unable without

assistance to travel even the short distance which still separated them,

far less to await much longer the fulfilment of the promises held out to

him.

By his subsequent admissions, it appears that for a considerable time he

lived entirely on Tycho's bounty, and by way of return, he wrote an

essay against Raimar, and against a Scotchman named Liddell, professor

at Rostoch and Helmstadt, who, like Raimar, had appropriated to himself

the credit of the Tychonic system. Kepler never adopted this theory, and

indeed, as the question merely regarded priority of invention, there

could be no occasion, in the discussion, for an examination of its

principles.

This was followed by a transaction, not much to Kepler's credit, who in

the course of the following year, and during a second absence from

Prague, fancied that he had some reason to complain of Tycho's

behaviour, and wrote him a violent letter, filled with reproaches and

insults. Tycho appears to have behaved in this affair with great

moderation: professing to be himself occupied with the marriage of his

daughter, he gave the care of replying to Kepler's charges, to Ericksen,

one of his assistants, who, in a very kind and temperate letter, pointed

out to him the ingratitude of his behaviour, and the groundlessness of

his dissatisfaction. His principal complaint seems to have been, that

Tycho had not sufficiently supplied his wife with money during his

absence. Ericksen's letter produced an immediate and entire change in

Kepler's temper, and it is only from the humble recantation which he

instantaneously offered that we learn the extent of his previous

violence. "Most noble Tycho," these are the words of his letter, "how

shall I enumerate or rightly estimate your benefits conferred on me! For

two months you have liberally and gratuitously maintained me, and my

whole family; you have provided for all my wishes; you have done me

every possible kindness; you have communicated to me everything you hold

most dear; no one, by word or deed, has intentionally injured me in

anything: in short, not to your children, your wife, or yourself have

you shown more indulgence than to me. This being so, as I am anxious to

put upon record, I cannot reflect without consternation that I should

have been so given up by God to my own intemperance, as to shut my eyes

on all these benefits; that, instead of modest and respectful gratitude,

I should indulge for three weeks in continual moroseness towards all

your family, in headlong passion, and the utmost insolence towards

yourself, who possess so many claims on my veneration from your noble

family, your extraordinary learning, and distinguished reputation.

Whatever I have said or written against the person, the fame, the

honour, and the learning of your excellency; or whatever, in any other

way, I have injuriously spoken or written, (if they admit no other more

favourable interpretation,) as to my grief I have spoken and written

many things, and more than I can remember; all and everything I recant,

and freely and honestly declare and profess to be groundless, false, and

incapable of proof." Hoffmann, the president of the states of Styria,

who had taken Kepler to Prague on his first visit, exerted himself to

perfect the reconciliation, and this hasty quarrel was entirely passed

over.

On Kepler's return to Prague, in September, 1601, he was presented to

the Emperor by Tycho, and honoured with the title of Imperial

Mathematician, on condition of assisting Tycho in his calculations.

Kepler desired nothing more than this condition, since Tycho was at that

time probably the only person in the world who possessed observations

sufficient for the reform which he now began to meditate in the theory

of astronomy. Rudolph appears to have valued both Tycho Brahe and Kepler

as astrologers rather than astronomers; but although unable to

appreciate rightly the importance of the task they undertook, of

compiling a new set of astronomical tables founded upon Tycho's

observations, yet his vanity was flattered with the prospect of his name

being connected with such a work, and he made liberal promises to defray

the expense of the new Rudolphine Tables. Tycho's principal assistant at

this time was Longomontanus, who altered his name to this form,

according to the prevalent fashion of giving to every name a Latin

termination. Lomborg or Longbierg was the name, not of his family, but

of the village in Denmark, where he was born, just as Müller was seldom

called by any other name than Regiomontanus, from his native town

Königsberg, as George Joachim Rheticus was so surnamed from Rhetia, the

country of the Grisons, and as Kepler himself was sometimes called

Leonmontanus, from Leonberg, where he passed his infancy. It was agreed

between Longomontanus and Kepler, that in discussing Tycho's

observations, the former should apply himself especially to the Moon,

and the latter to Mars, on which planet, owing to its favourable

position, Tycho was then particularly engaged. The nature of these

labours will be explained when we come to speak of the celebrated book

"On the Motions of Mars."

This arrangement was disturbed by the return of Longomontanus into

Denmark, where he had been offered an astronomical professorship, and

still more by the sudden death of Tycho Brahe himself in the following

October. Kepler attended him during his illness, and after his death

undertook to arrange some of his writings. But, in consequence of a

misunderstanding between him and Tycho's family, the manuscripts were

taken out of his hands; and when, soon afterwards, the book appeared,

Kepler complained heavily that they had published, without his consent

or knowledge, the notes and interlineations added by him for his own

private guidance whilst preparing it for publication.

On Tycho's death, Kepler succeeded him as principal mathematician to the

emperor; but although he was thus nominally provided with a liberal

salary, it was almost always in arrear. The pecuniary embarrassments in

which he constantly found himself involved, drove him to the resource of

gaining a livelihood by casting nativities. His peculiar temperament

rendered him not averse from such speculations, and he enjoyed

considerable reputation in this line, and received ample remuneration

for his predictions. But although he did not scruple, when consulted, to

avail himself in this manner of the credulity of his contemporaries, he

passed over few occasions in his works of protesting against the

futility of this particular genethliac astrology. His own astrological

creed was in a different strain, more singular, but not less

extravagant. We shall defer entering into any details concerning it,

till we come to treat of his book on Harmonics, in which he has

collected and recapitulated the substance of his scattered opinions on

this strange subject.

His next works deserving notice are those published on occasion of the

new star which shone out with great splendour in 1604, in the

constellation Cassiopeia.[181] Immediately on its appearance, Kepler

wrote a short account of it in German, marked with all the oddity which

characterises most of his productions. We shall see enough of his

astronomical calculations when we come to his book on Mars; the

following passage will probably be found more amusing.

After comparing this star with that of 1572, and mentioning that many

persons who had seen it maintained this to be the brighter of the two,

since it was nearly twice the size of its nearest neighbour, Jupiter, he

proceeds as follows:—"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;[182] 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

place 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 out of his own accord—'Here we have him!'—What it

may portend is hard to determine, and thus much only is certain, that it

comes to tell mankind either nothing at all, or high and weighty 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 intrusted 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."

It would hardly be supposed, from the tenor of this last passage, that

the writer of it was not a determined enemy to astrological predictions

of every description. In 1602 he had published a disputation, not now

easily met with, "On the Principles of Astrology," in which it seems

that he treated the professed astrologers with great severity. The

essence of this book is probably contained in the second treatise on the

new star, which he published in 1606.[183] In this volume he inveighs

repeatedly against the vanity and worthlessness of ordinary astrology,

declaring at the same time, that the professors of that art know that

this judgment is pronounced by one well acquainted with its principles.

"For if the vulgar are to pronounce who is the best astrologer, my

reputation is known to be of the highest order; if they prefer the

judgment of the learned, they are already condemned. Whether they stand

with me in the eyes of the populace, or I fall with them before the

learned, in both cases I am in their ranks; I am on a level with them; I

cannot be renounced."

The theory which Kepler proposed to substitute is intimated shortly in

the following passage: "I maintain that the colours and aspects, and

conjunctions of the planets, are impressed on the natures or faculties

of sublunary things, and when they occur, that these are excited as well

in forming as in moving the body over whose motion they preside. Now let

no one conceive a prejudice that I am anxiously seeking to mend the

deplorable and hopeless cause of astrology by far-fetched subtilties and

miserable quibbling. I do not value it sufficiently, nor have I ever

shunned having astrologers for my enemies. But a most unfailing

experience (as far as can be hoped in natural phenomena) of the

excitement of sublunary natures by the conjunctions and aspects of the

planets, has instructed and compelled my unwilling belief."

After exhausting other topics suggested by this new star, he examines

the different opinions on the cause of its appearance. Among others he

mentions the Epicurean notion, that it was a fortuitous concourse of

atoms, whose appearance in this form was merely one of the infinite

number of ways in which, since the beginning of time, they have been

combined. Having descanted for some time on this opinion, and declared

himself altogether hostile to it, Kepler proceeds as follows:—"When I

was a youth, with plenty of idle time on my hands, I was much taken with

the vanity, of which some grown men are not ashamed, of making anagrams,

by transposing the letters of my name, written in Greek, so as to make

another sentence: out of Ιωάννης Κεπλῆρος I made Σειρήνων κάπηλος;[184]

in Latin, out of _Joannes Keplerus_ came _Serpens in akuleo_.[185] But

not being satisfied with the meaning of these words, and being unable to

make another, I trusted the thing to chance, and taking out of a pack of

playing cards as many as there were letters in the name, I wrote one

upon each, and then began to shuffle them, and at each shuffle to read

them in the order they came, to see if any meaning came of it. Now, may

all the Epicurean gods and goddesses confound this same chance, which,

although I spent a good deal of time over it, never showed me anything

like sense even from a distance.[186] So I gave up my cards to the

Epicurean eternity, to be carried away into infinity, and, it is said,

they are still flying about there, in the utmost confusion among the

atoms, and have never yet come to any meaning. I will tell these

disputants, my opponents, not my own opinion, but my wife's. Yesterday,

when weary with writing, and my mind quite dusty with considering these

atoms, I was called to supper, and a salad I had asked for was set

before me. It seems then, said I aloud, that if pewter dishes, leaves of

lettuce, grains of salt, drops of water, vinegar, and oil, and slices of

egg, had been flying about in the air from all eternity, it might at

last happen by chance that there would come a salad. Yes, says my wife,

but not so nice and well dressed as this of mine is."

FOOTNOTES:

[181] See Life of Galileo, p. 16.

[182] The fiery trigon occurs about once in every 800 years, when

Saturn, Jupiter, and Mars are in the three fiery signs, Aries, Leo, and

Sagittarius.

[183] The copy of this work in the British Museum is Kepler's

presentation copy to our James I. On the blank leaf, opposite the

title-page, is the following inscription, apparently in the author's

hand-writing:—"Regi philosophanti, philosophus serviens, Platoni

Diogenes, Britannias tenenti, Pragæ stipem mendicans ab Alexandro, e

dolio conductitio, hoc suum philosophema misit et commendavit."

[184] The tapster of the Sirens.

[185] A serpent in his sting.

[186] In one of his anonymous writings Kepler has anagrammatized his

name, _Joannes Keplerus_, in a variety of other forms, probably selected

from the luckiest of his shuffles:—"_Kleopas Herennius, Helenor

Kapuensis, Raspinus Enkeleo, Kanones Pueriles._"

CHAPTER III.

_Kepler publishes his Supplement to Vitellion—Theory of

Refraction._

DURING several years Kepler remained, as he himself forcibly expressed

it, begging his bread from the emperor at Prague, and the splendour of

his nominal income served only to increase his irritation, at the real

neglect under which he nevertheless persevered in his labours. His

family was increasing, and he had little wherewith to support them

beyond the uncertain proceeds of his writings and nativities. His salary

was charged partly on the states of Silesia, partly on the imperial

treasury; but it was in vain that repeated orders were procured for the

payment of the arrears due to him. The resources of the empire were

drained by the constant demands of an engrossing war, and Kepler had not

sufficient influence to enforce his claims against those who thought

even the smallest sum bestowed upon him ill spent, in fostering

profitless speculations. In consequence of this niggardliness, Kepler

was forced to postpone the publication of the Rudolphine Tables, which

he was engaged in constructing from his own and Tycho Brahe's

observations, and applied himself to other works of a less costly

description. Among these may be mentioned a "Treatise on Comets,"

written on occasion of one which appeared in 1607: in this he suggests

that they are planets moving in straight lines. The book published in

1604, which he entitles "A Supplement to Vitellion," may be considered

as containing the first reasonable and consistent theory of optics,

especially in that branch of it usually termed dioptrics, which relates

to the theory of vision through transparent substances. In it was first

explained the true use of the different parts of the eye, to the

knowledge of which Baptista Porta had already approached very nearly,

though he stopped short of the accurate truth. Kepler remarked the

identity of the mechanism in the eye with that beautiful invention of

Porta's, the camera obscura; showing, that the light which falls from

external objects on the eye is refracted through a transparent

substance, called, from its form and composition, the crystalline lens,

and makes a picture on the fine net-work of nerves, called the retina,

which lies at the back of the eye. The manner in which the existence of

this coloured picture on the retina causes to the individual the

sensation of sight, belongs to a theory not purely physical; and beyond

this point Kepler did not attempt to go.

The direction into which rays of light (as they are usually called) are

bent or refracted in passing through the air and other transparent

substances or mediums, is discussed in this treatise at great length.

Tycho Brahe had been the first astronomer who recognized the necessity

of making some allowance on this account in the observed heights of the

stars. A long controversy arose on this subject between Tycho Brahe and

Rothman, the astronomer at Hesse Cassel, a man of unquestionable talent,

but of odd and eccentric habits. Neither was altogether in the right,

although Tycho had the advantage in the argument. He failed however to

establish the true law of refraction, and Kepler has devoted a chapter

to an examination of the same question. It is marked by precisely the

same qualities as those appearing so conspicuously in his astronomical

writings:—great ingenuity; wonderful perseverance; bad philosophy. That

this may not be taken solely upon assertion, some samples of it are

subjoined. The writings of the authors of this period are little read or

known at the present day; and it is only by copious extracts that any

accurate notion can be formed of the nature and value of their labours.

The following tedious specimen of Kepler's mode of examining physical

phenomena is advisedly selected to contrast with his astronomical

researches: though the luck and consequently the fame that attended his

divination were widely different on the two occasions, the method

pursued was the same. After commenting on the points of difference

between Rothman and Tycho Brahe, Kepler proceeds to enumerate his own

endeavours to discover the law of refraction.

"I did not leave untried whether, by assuming a horizontal refraction

according to the density of the medium, the rest would correspond with

the sines of the distances from the vertical direction, but calculation

proved that it was not so: and indeed there was no occasion to have

tried it, for thus the refractions would increase according to the same

law in all mediums, which is contradicted by experiment.