Chapter III: Part 3

Lastly, I must not pass over the consideration of the reason why it happens that the Medicean stars, in performing very small revolutions about Jupiter, seem sometimes more than twice as large as at other times. We can by no means look for the explanation in the mists of the Earth’s atmosphere, for they appear increased or diminished, while the discs of Jupiter and neighbouring fixed stars are seen quite unaltered. That they approach and recede from the Earth at the points of their revolutions nearest to and furthest from the Earth to such an extent as to account for so great changes seems altogether untenable, for a strict circular motion can by no means show those phenomena; and an elliptical motion (which in this case would be nearly rectilinear) seems to be both untenable and by no means in harmony with the phenomena observed. But I gladly publish the explanation which has occurred to me upon this subject, and submit it to the judgment and criticism of all true philosophers. It is certain that when atmospheric mists intervene the Sun and Moon appear larger, but the fixed stars and planets less than they really are; hence the former luminaries, when near the horizon, are larger than at other times, but stars appear smaller, and are frequently scarcely visible; also they are still more diminished if those mists are bathed in light; so stars appear very small by day and in the twilight, but the Moon does not appear so, as I have previously remarked. Moreover, it is certain that not only the Earth, but also the Moon, has its own vaporous sphere enveloping it, for the reasons which I have previously mentioned, and especially for those which shall be stated more fully in my _System_; and we may consistently decide that the same is true with regard to the rest of the planets; so that it seems to be by no means an untenable opinion to place round Jupiter also an atmosphere denser than the rest of the ether,[18] about which, like the Moon about the sphere of the elements, the Medicean planets (Jupiter’s satellites) revolve; and that by the intervention of this atmosphere they appear smaller when they are in apogee; but when in perigee, through the absence or attenuation of that atmosphere, they appear larger. Want of time prevents my going further into these matters; my readers may expect further remarks upon these subjects in a short time.

[18] Modern astronomers agree in assigning an atmosphere to
Jupiter, but consider it not extensive enough to affect the
brightness of the satellites.—(WEBB, _Celestial Objects for Common
Telescopes_.) Their absolute magnitudes are different, and their
surfaces have been observed to be obscured by spots, which may
account for the variations of their brightness. These spots, like
the lunar spots, are probably due to variations of reflective
power at different parts of their surfaces, for as they always
turn the same face to Jupiter, they present different portions of
their surfaces to us periodically, and it has been ascertained
by observation that “these fluctuations in their brightness are
periodical, depending on their position with respect to the
Sun.”—(HERSCHEL, _Outlines of Astronomy_; ARAGO, _Astronomie
Populaire_, 1854.)

_Original Configurations of Jupiter’s Satellites observed by Galileo in the months of January, February, and March 1610, and published with the 1st edition of his book_ Sidereus Nuncius, _Venice, 1610._

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FIG. | DATE. | EAST. | WEST.
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1 | Jan. 7 |
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2 | 8 |
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3 | 10 |
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4 | 11 |
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5 | 12 |
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6 | 13 |
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7 | 15 | •
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12 | 18 |
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30 | Jan. 31 | •
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31 | Feb. 1 |
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32 | 2 |
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40 | 9 |
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41 | 10 |
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43 | 11 | •
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56 | 25 |
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59 | 26 | • ◯ • •
| | ⨀ Star.
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60 | 27 | • • ◯ • •
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61 | 28 | • ◯ •
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62 | 28 |
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63 | Mar. 1 | •
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64 | 2 | •
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A PART OF THE PREFACE TO
KEPLER’S DIOPTRICS

FORMING

_A CONTINUATION OF GALILEO’S
SIDEREAL MESSENGER._

In the preface to Kepler’s _Dioptrics_ there are introduced letters
of Galileo about the new and astonishing discoveries which he
had made in the heavens by the aid of the telescope since the
publication of his work, _The Sidereal Messenger_. The portion
of the preface which refers to Galileo, containing these letters
and Kepler’s remarks upon them, is added here, as continuing the
original account of Galileo’s astronomical discoveries.

_Extract from the Preface of Kepler’s Dioptrics. Augsburg, 1611._

[Sidenote: Kepler remarks on the importance of the application of the telescope to astronomical investigations as indicated by Galileo’s discoveries, published in his _Sidereal Messenger_.]

“_The Sidereal Messenger_” of Galileo has been for a long time in everybody’s hands, also my “_Discussion_, such as it is, _with this Messenger_,” and my _Brief Narrative_ in confirmation of Galileo’s _Sidereal Messenger_, so any reader may briefly weigh the chief points of that _Messenger_ and see the nature and the value of the discoveries made by the aid of the telescope, the theory of which I am intending to demonstrate in this treatise. Actual sight testified that there is a certain bright heavenly body which we call the Moon. It was demonstrated from the laws of optics that this body is round; also Astronomy, by some arguments founded upon optics, had built up the conclusion that its distance from the earth is about sixty semi-diameters of the earth. Various spots showed themselves in that body; and the result was a dubious opinion among a few philosophers, derived from Hecatæus’ account of the stories about the island of the Hyperboreans,[19] that the reflected images of mountains and valleys, sea and land, were seen there; but now the telescope places all these matters before our eyes in such a way that he must be an intellectual coward who, while enjoying such a view, still thinks that the matter is open to doubt. Nothing is more certain than that the southern parts of the moon teem with mountains, very many in number, and vast in size; and that the northern parts, inasmuch as they are lower, receive in most extensive lakes the water flowing down from the south. The conclusions which previously Pena published as disclosed by the aid of optics, started indeed from certain slight supports, rather than foundations, afforded by actual sight, but were proved by long arguments depending one upon another, so that they might be assigned to human reason rather than to sight; but now our very eyes, as if a new door of heaven had been opened, are led to the view of matters once hidden from them. But if it should please any one to exhaust the force of reasoning upon these new observations, who does not see how far the contemplation of nature will extend her boundaries, when we ask, “What is the use of the tracts of mountains and valleys, and the very wide expanse of seas in the moon?” and “May not some creature less noble than man be imagined such as might inhabit those tracts?”

[19] Diodorus Siculus, ii. 47.

With no less certainty also do we decide by the use of this instrument even that famous question, which, coeval with philosophy itself, is disputed to this day by the noblest intellects—I mean, whether the earth can move (as the theory of the Planets greatly requires) without the overthrow of all bodies that have weight, or the confusion of the motion of the elements? For if the earth were banished from the centre of the universe, some fear lest the water should leave the orb of the earth and flow to the centre of the universe; and yet we see that in the moon, as well as in the earth, there is a quantity of moisture occupying the sunken hollows of that globe; and although this orb revolves actually in the ether, and outside the centres not merely of the universe, but even of our earth, yet the mass of water in the moon is not at all hindered from cleaving invariably to the orb of the moon, and tending to the centre of the body to which it belongs. So, by this instance of the phenomena of the moon, the science of optics amends the received theory of mechanics, and confirms on this point my introduction to my _Commentaries upon the Motions of the Planet Mars_.[20]

[20] Kepler says in his introduction to his _Commentaries upon
the Motions of the Planet Mars_, that the theory of gravitation
depends on certain axioms, one of which is that “heavy bodies do
not tend to the centre of the universe, supposing the earth to be
placed there, because that point is the centre of the universe,
but because it is the centre of the earth. So, wherever the earth
be set, or whithersoever it be transported, heavy bodies have a
continual tendency to it.” Kepler’s object in this work was to
correct the methods for determining the apparent places of the
planets according to the three theories then current—the Ptolemaic,
the Copernican, and that of Tycho Brahe.

In 1593 the observed place of the planet Mars differed by nearly
5° from the place calculated for it. Kepler accordingly studied
the motions of this planet, and “by most laborious demonstrations
and discussions of many observations,” arrived at the conclusions
known as Kepler’s first and second laws; according to which the
Copernican system of eccentrics and epicycles was replaced by an
ellipse whose centre and eccentricity were the same as the centre
and eccentricity of the eccentric in the older method, and the Sun
therefore was in one of the foci. Also the motion of the planet in
its orbit was such that equal areas were described about the Sun by
the radius vector of the planet in equal times.—KEPLER, _Astronomia
Nova_ αἰτιολογητός (Prague), 1609.

The followers of the Samian philosophy (for I may use this epithet to designate the philosophy originated by the Samians, Pythagoras and Aristarchus) have a strong argument against the apparent immobility of the earth provided in the phenomena of the moon. For we are taught by optics that if any one of us was in the moon, to him the moon, his abode, would seem quite immovable, but our earth and sun and all the rest of the heavenly bodies movable; for the conclusions of sight are thus related.

Pena has noticed how astronomers, using the principles of optics, have by most laborious reasoning removed the Milky Way from the elementary universe, where Aristotle had placed it, into the highest region of the ether; but now, by the aid of the telescope lately invented, the very eyes of astronomers are conducted straight to a thorough survey of the substance of the Milky Way; and whoever enjoys this sight is compelled to confess that the Milky Way is nothing else but a mass of extremely small stars.

Again, up to this time the nature of nebulous stars had been entirely unknown; but if the telescope be directed to one of such nebulous balls, as Ptolemy calls them, it again shows, as in the case of the Milky Way, three or four very bright stars clustered very close together.

Again, who without this instrument would have believed that the number of the fixed stars was ten times, or perhaps twenty times, more than that which is given in Ptolemy’s description of the fixed stars? And whence, pray, should we seek for conclusive evidence about the end or boundary of this visible universe, proving that it is actually the sphere of the fixed stars, and that there is nothing beyond, except from this very discovery by the telescope of this multitude of fixed stars, which is, as it were, the vaulting of the mobile universe? Again, how greatly an astronomer would go wrong in determining the magnitude of the fixed stars, except he should survey the stars all over again with a telescope, also may be seen in Galileo’s treatise, and we will also hereafter produce in proof a letter from a German astronomer.

But no words can express my admiration of that chapter of the _Sidereal Messenger_ where the story is told of the discovery, by the aid of a very highly finished telescope, of another world, as it were, in the planet Jupiter. The mind of the philosopher almost reels as he considers that there is a vast orb, which is equal in mass to fourteen orbs like the earth (unless on this point the telescope of Galileo shall shortly reveal something more exact than the measurements of Tycho Brahe) round which circle four moons, not unlike this moon of ours; the slowest revolving in the space of fourteen of our days, as Galileo has published; the next to this, by far the brightest of the four, in the space of eight days, as I detected in last April and May; the other two in still shorter periods. And here the reasoning of my _Commentaries about the Planet Mars_, applied to a similar case, induces me to conclude also that the actual orb of Jupiter rotates with very great rapidity, most certainly faster than once in the space of one of our days; so that this rotation of the mighty orb upon its own axis is accompanied wherever it goes by the perpetual circuits of those four moons. Moreover, this sun of ours, the common source of heat and light for this terrestrial world as well as for that world of Jupiter, which we consider to be of the angular magnitude of 30´ at most, there scarcely subtends more than 6´ or 7´, and is found again in the same position among the fixed stars, having completed the zodiac in the interval, after a period of twelve of our years.[21] Accordingly, the creatures which live on that orb of Jupiter, while they contemplate the very swift courses of those four moons among the fixed stars, while they behold them and the sun rising and setting day by day, would swear by Jupiter-in-stone, like the Romans (for I have lately returned from those parts), that their orb of Jupiter remains immovable in one spot, and that the fixed stars and the sun, which are the bodies really at rest, no less than those four moons of theirs, revolve round that abode of theirs with manifold variety of motions. And from this instance now, much more than before from the instance of the moon, any follower of the Samian philosophy will learn what reply may be made to any one objecting to the theory of the motion of the earth as absurd, and alleging the evidence of our sight. O telescope, instrument of much knowledge, more precious than any sceptre! Is not he who holds thee in his hand made king and lord of the works of God? Truly

“All that is overhead, the mighty orbs
With all their motions, thou dost subjugate
To man’s intelligence.”

If there is any one in some degree friendly to Copernicus and the lights of the Samian philosophy, who finds this difficulty only, that he doubts how it can happen, supposing the earth to perform again and again her course among the planets through the ethereal plains, that the moon should keep so constantly by her side, like an inseparable companion, and at the same time fly round and round the actual orb of the earth, just like a faithful dog which goes round and round his master on some journey, now running in front, now deviating to this side or that, in ever-varying mazes, let him look at the planet Jupiter, which, as this telescope shows, certainly carries in its train not one such companion only, like the earth, as Copernicus showed, but actually four, that never leave it, though all the time hastening each in its own orbit.

[21] The degree of accuracy attained by Kepler and Galileo with
their imperfect instruments will be appreciated by comparing
these statements with the determinations of later astronomers.
Jupiter is about 1300 times the size of the Earth. Its diameter is
about 87,000 miles; time of rotation, 9 h. 55 m. 21 sec.; time of
revolution, 4333 days nearly. The angular diameter of the sun, seen
from Jupiter, is between 6´ and 7´. The times of revolution of the
four satellites are, as already given: (i.) 1 d. 18 h. 28 m., (ii.)
3 d. 13 h. 15 m., (iii.) 7 d. 3 h. 43 m., (iv.) 16 d. 16 h. 32 m.

But enough has been said about these matters in my _Discussion with the Sidereal Messenger_. It is time that I should turn to those discoveries which have been made since the publication of Galileo’s _Sidereal Messenger_, and since my _Discussion_ with it, by means of this telescope.

[Sidenote: Galileo’s discovery of Saturn’s ring (imperfectly).]

It is now just a year since Galileo wrote to Prague, and gave full notice that he had detected something new in the heavens beyond his former discoveries; and that there might not be any one who, with the intention of detracting from his credit, should try to pass himself off as an earlier observer of the phenomenon, Galileo gave a certain space of time for the publication of the new phenomena which any one had seen; he himself meanwhile described his discovery in letters transposed in this manner: _s m a i s m r m i l m e p o e t a l e u m i b u n e n u g t t a u i r a s_. Out of these letters I made an uncouth verse which I inserted in my _Short Account_ in the month of September of last year:—

Salve umbistineum[22] geminatum Martia proles.
Hail, twin companionship, children of Mars.

[22] _Umbistineum._ Apparently this is some German word with a
Latin ending, such as _um-bei-stehn_; Kepler fancied that Galileo
had discovered two satellites of Mars.

But I was a very long way from the meaning of the letters; it contained nothing to do with Mars; and, not to detain you, reader, here is the solution of the riddle in the words of Galileo himself, the author of it:[23]—

“_Di Firenze li 13 di Novembre 1610._—Ma passando ad altro, giacchè
il Sig. Keplero ha in questa sua ultima narrazione stampate le
lettere che io mandai trasposte a Vostra Signoria Illustrissima
e Reverendissima venendomi anco significato come Sua Maestà
ne desidera il senso, ecco che io lo mando a Vostra Signoria
Illustrissima per participarlo con Sua Maestà col Sig. Keplero e
con chi piacerà a Vostra Signoria Illustrissima bramando io che
lo sappia ognuno. Le lettere dunque combinate nel lor vero senso
dicono così,

Altissimum planetam tergeminum observavi.

Questo è, che Saturno con mia grandissima ammirazione ho osservato
essere non una stella sola, ma tre insieme, le quali quasi si
toccano; e sono trà di loro totalmente immobili, e constituite
in questa guisa o◯o. Quella di mezzo è assai più grande delle
laterali; sono situate una da oriente, l’altra da occidente, nella
medesima linea retta a capello; non sono giustamente secondo la
dirittura del Zodiaco, ma l’occidentale si eleva alquanto verso
Borea; forse sono parallele all’Equinoziale. Se si guarderanno
con un occhiale che non sia di grandissima moltiplicazione, non
appariranno tre stelle ben distinte, ma parrà, che Saturno sia una
stella lunghetta in forma di un’oliva, così, ☾☽. Ma servendosi
di un occhiale che moltiplichi più di mille volte in superficie,
si vedranno tre globi distintissimi, che quasi si toccano, non
apparendo trà essi maggior divisione di un sottil filo oscuro. Or
ecco trovata la corte a Giove, e due Servi a questo Vecchio che
l’aiutano a camminare nè mai se gli staccano dal fianco. Intorno
agli altri Pianeti non ci è novità alcuna, ec.”

[23] The text of the four letters of Galileo followed here is that
given in the edition of Galileo’s works published at Florence,
1842-56; that in the edition of Kepler’s _Dioptrics_, published at
Augsburg, 1611, is very inaccurate. These letters were written to
Giuliano de’ Medici, ambassador of the Grand-Duke of Tuscany to the
Emperor Rudolf II. at Prague.

Although these words differ little from Latin, yet I will translate them that no difficulty may hinder my reader from following me. Thus then Galileo writes:—“But to come now to my second topic. Since Kepler has published in that recent ‘_Narrative_’ of his the letters which I sent as an anagram to your illustrious Lordship, and since an intimation has been given me that his Majesty desires to be taught the meaning of those letters, I send it to your illustrious Lordship, that your Lordship may communicate it to his Majesty, to Kepler, and to any one your Lordship may wish.

“The letters when joined together as they ought to be, say this,

‘Altissimum planetam tergeminum observavi,’

‘I have observed the most distant of the planets to have a triple
form.’

“For in truth I have found out with the most intense surprise
that the planet Saturn is not merely one single star, but three
stars very close together, so much so that they are all but in
contact one with another. They are quite immovable with regard to
each other, and are arranged in this manner, o◯o. The middle star
of the three is by far greater than the two on either side. They
are situated one towards the east, the other towards the west, in
one straight line to a hair’s-breadth; not, however, exactly in
the direction of the Zodiac, for the star furthest to the west
rises somewhat towards the north; perhaps they are parallel to
the equator. If you look at them through a glass that does not
multiply much, the stars will not appear clearly separate from one
another, but Saturn’s orb will appear somewhat elongated, of the
shape of an olive, thus, ☾☽. But if you should use a glass which
multiplies a surface more than a thousand times, there will appear
very distinctly three orbs, almost touching one another; and they
will be thought to be not farther apart than the breadth of a very
fine and scarcely visible thread. So you see a guard of satellites
has been found for Jupiter, and for the decrepit little old man two
servants to help his steps and never leave his side. Concerning the
rest of the planets I have found nothing new.”

So says Galileo; but if I may do so, I will not make an old dotard out of Saturn, and two servants for him out of his companion orbs, but rather out of those three united bodies I will make a triple Geryon, out of Galileo Hercules, and out of the telescope his club, armed with which, Galileo has conquered that most distant of the planets, drawn it out of the furthest recesses of nature, dragged it down to earth, and exposed it to the gaze of us all. It pleases me too, now that the nest has been found, to consider with curiosity what kind of brood must be in it, what kind of life, if there be any life there, between orbs which all but touch each other two and two, where not even

“a space
Of sky extends not more than three ells wide,”[24]

but where there is scarcely a chink of a nail’s-breadth all round.

[24] Virgil, _Eclog._ iii. 105.

Do indeed the astrologers rightly ascribe to Saturn the guardianship of miners, who, accustomed to spend their lives, like moles, underground, seldom breathe the free air under the open sky? Although the darkness here is rather more supportable than in Saturn, because the sun, which appears there only as large as Venus appears to us on the earth, continually casts its rays through the spaces between the different orbs in such a way that those inhabitants who are situated on one orb are covered by the other as by a ceiling; while those on the latter orb, on the top of this roof of theirs, exposed as it is to the full light of the sun, receive a glare as if from very firebrands. But I must draw in the reins and check my mind in its enjoyment of the free fields of ether; for fear, perchance, later observations should report something different from the first account, something changed in course of time.[25]

[25] The completion of Galileo’s observations on Saturn depended
on the improvement of astronomical instruments, as will be evident
from the following sketch. Galileo made out the first indications
of Saturn’s ring in 1610, as narrated in his letter, with a power
of thirty; but in December 1612 he wrote to one of his friends,
Marco Velseri, that he could no longer see these indications,
and began to imagine that his telescope had deceived him, and
apparently abandoned further researches. Hevelius in 1642 saw
the ring more clearly, but figured it as two crescents attached
to Saturn by their cusps. At length, in 1653, Huyghens provided
himself with a power of one hundred, having made the lenses with
his own hands, and immediately discovered the explanation of the
phenomena which had baffled previous observers. He published his
explanation of Saturn’s ring, and his discovery of the first
satellite, in his _Systema Saturnium_, 1659. Cassini, with still
more powerful instruments, discovered four more satellites in
1671, 1672, 1684. Sir William Herschel in 1789 detected two
more, “which can only be seen with telescopes of extraordinary
power and perfection, and under the most favourable atmospheric
circumstances.”—(HERSCHEL, _Outlines of Astronomy_, § 548.) And the
last of the eight satellites was discovered in 1848 by Lassell of
Liverpool, and Bond of Cambridge, U.S., simultaneously.

At the end of his letter Galileo seemed to think that he had come to the end of his reports about the planets, and observations of new phenomena respecting them, but ever on the watch, that eye of his, that one not of Nature’s making—I mean his telescope—in a short time made more discoveries, concerning which read the following letter of Galileo:—

[Sidenote: Account of Galileo’s discovery of the phases of Venus.]

“_Di Firenze li 11 di Decembre 1610._—Sto con desiderio, attendendo
la risposta a due mie scritte ultimamente per sentire quello, che
averà detto il Sig. Keplero della stravaganza di Saturno. Intanto
mando [a Vostra Signoria Illustrissima e Reverendissima] la cifra
di un altro particolare osservato da me nuovamente, il quale si
tira dietro la decisione di grandissime controversie in Astronomia,
ed in particolare contiene in se un gagliardo argomento per la
constitutione [Pitagorica e Copernicana] dell’Universo; e a suo
tempo pubblicherò la deciferazione ed altri particolari. Spero che
averò trovato il metodo per definire i periodi dei quattro Pianeti
Medicei, stimati con gran ragione quasi inesplicabili dal Sig.
Keplero, al quale piacerà, ec.

“Le lettere trasposte sono queste:

“Haec immatura a me jam frustra leguntur, o.y.”

Which may be translated thus:—

“I am anxiously looking for an answer to my last two letters, that
I may learn what Kepler says about the marvels of Saturn’s orb.
In the meantime I send him a riddle concerning a certain new and
splendid observation which tends to decide great controversies in
astronomy; and especially contains a fine argument in favour of the
Pythagorean and Copernican system of the universe. At the proper
time I will publish the solution of the riddle, and some other
particulars. I hope that I have found a method of determining the
periodic times of the four Medicean planets, which Kepler, not
without very good reason, thought inexplicable, etc.

“The letters turned into an anagram, are these:

“Haec immatura a me jam frustra leguntur, o.y.”

So far Galileo. But if, reader, this letter has filled you with a desire to know the meaning contained in those letters, then you must read another letter of Galileo which follows.

_E the Earth (centre of universe). S the Sun. C centre of eccentric. D centre of planet’s epicycle. VV' stationary points. s v v' projections of SVV' on the ecliptic of which E is the centre._]

_S the Sun, centre of solar system. v e positions of planet and Earth at conjunction. VV' stationary points of planet. EE' corresponding positions of the Earth._]

But before you do so, I should like you to notice, by the way, what Galileo says about the Pythagorean and Copernican system of the universe. For he points to my _Mystery of the Universe_,[26] published fourteen years ago, in which I took the dimensions of the Planetary orbits according to the astronomy of Copernicus, who makes the sun immovable in the centre, and the earth movable both round the sun and upon its own axis; and I showed that the differences of their orbits corresponded to the five regular Pythagorean figures, which had been already distributed by their author among the elements of the world, though the attempt was admirable rather than happy or legitimate, and for which figures’ sake Euclid wrote the whole of his Geometry. Now, in that _Mystery_ you may find a sort of combination of Astronomy and Euclid’s Geometry, and through this combination a most thorough completion and finishing of them both; and this was the reason why I waited with intense longing to see what sort of an argument Galileo would produce in favour of the Pythagorean system of the universe. After this explanation, Galileo’s letter about this argument was as follows:—

[26] Kepler, in his _Mystery of the Universe_, endeavoured to
connect the orbits of the planets with the five regular solids,
thus: If in a sphere (i.) a cube be inscribed, and in the cube
a sphere (ii.); and in that sphere a tetrahedron, and in the
tetrahedron a sphere (iii.); and in that sphere a dodecahedron,
and in the dodecahedron a sphere (iv.); and in that sphere an
icosahedron, and in the icosahedron a sphere (v.); and in that
sphere an octahedron, and in the octahedron a sphere (vi.),
the diameters of these six spheres will be proportional to the
diameters of the orbits of Saturn, Jupiter, Mars, the Earth, Venus,
and Mercury respectively; or, as Kepler expresses it, the common
centre of these spheres represents the position of the Sun, and the
six spheres represent the spheres of the planets.

By these considerations, however, Kepler was led to enunciate
his third law, that the squares of the periodic times of planets
are proportional to the cubes of their mean distances from the
sun.—KEPLER, _Prodromus Dissertationum Mathematicarum continens
Mysterium Cosmographicum, etc._ (Tübingen, 1596.)

“Illustrissimo e Reverendissimo Signore mio colendissimo.

“È tempo che io deciferi a Vostra Signoria Illustrissima e
Reverendissima e per lei al Sig. Keplero le lettere trasposte
le quali alcune settimane sono le inviai; è tempo dico, giacchè
sono interamente chiaro della verità del fatto, sicchè non ci
resta un minimo scrupolo, o dubbio. Sapranno dunque come circa a
tre mesi fa vedendosi Venere vespertina la cominciai ad osservar
diligentemente coll’occhiale, per veder col senso stesso
quello di che non dubitava punto l’intelletto. La vidi dunque sul
principio di figura rotonda, pulita e terminata, ma molto picciola;
di tal figura si mantenne sino che cominciò ad avvicinarsi alla
sua massima digressione, ma tra tanto andò crescendo in mole.
Cominciò poi a mancare dalla rotondità nella sua parte orientale
ed avversa al Sole, e in pochi giorni si ridusse ad esser un mezzo
cerchio perfettissimo, e tale si mantenne, senza punto alterarsi,
finchè incominciò à ritirarsi verso il Sole, allontanandosi
dalla tangente. Ora va calando dal mezzo cerchio, e si mostra
cornicolata, e anderà assottigliandosi sino all’occultazione,
riducendosi allora con corna sottilissime. Quindi passando all’
apparizione mattutina, la vedremo pur falcata, e sottilissima e
colle corna avverse al Sole; anderà poi crescendo fino alla massima
digressione, dove apparirà semicircolare, e tale senza alterarsi si
manterrà molti giorni, e poi dal mezzo cerchio passerà presto al
tutto tondo, e così rotonda si conserverà poi per molti mesi. Il
suo diametro adesso è circa cinque volte maggiore di quello, che
si mostrava nella sua prima apparizione vespertina; dalla quale
mirabile esperienza abbiamo sensata, e certa dimostrazione di due
gran questioni state fin qui dubbie trà i maggiori ingegni del
Mondo. L’una è, che i Pianeti tutti son di lor natura tenebrosi
(accadendo anco a Mercurio l’istesso, che a Venere). L’altra, che
Venere necessarissimamente si volge intorno al Sole, come anco
Mercurio, cosa, che degli altri Pianeti, fu creduta da’ Pitagorici,
dal Copernico, dal Keplero e da’ loro seguaci, ma non sensatamente
provata, come ora in Venere, ed in Mercurio.

“Averanno dunque il Sig. Keplero, e gli altri Copernicani da
gloriarsi di aver creduto e filosofato bene, sebbene ci è toccato,
e ci è per toccare ancora ad esser reputati dall’ università dei
Filosofi in libris, per poco intendenti, e poco meno che stolti.

“Le parole dunque, che mandai trasposte, e che dicevano,

Haec immatura a me jam frustra leguntur, o.y.

dicono ordinate

Cynthiae figuras aemulatur mater amorum.

“Cioè, che Venere imita le figure della Luna. Osservai tre notti
sono l’ecclisse, nella quale non vi è cosa notabile, solo si vede
il taglio dell’ombra indistinto, confuso e come annebbiato,
e questo per derivare essa ombra dalla Terra lontanissima da
essa Luna. Voleva scrivere altri particolari, ma essendo stato
trattenuto molto da alcuni gentiluomini, ed essendo l’ora
tardissima, son forzato a finire. Favoriscami salutare in mio nome
i SS. Keplero, Asdale e Segheti, ed a Vostra Signoria Illustrissima
con ogni reverenza bacio le mani, e dal Signore Dio gli prego
felicità. Di Firenze il primo di Gennaio 1610. Ab Incarnatione.

“Di Vostra Signoria Illustrissima e Reverendissima Servidore
obbligatissimo.

Galileo Galilei.”

Such is Galileo’s letter; but let me give you the substance of it:—

“It is time for me to disclose the method of reading the letters
which some weeks since I sent you as an anagram. It is time now, I
mean, after I have become quite certain about the matter, so much
so that I have no longer even a shadow of doubt. You must know then
that about three months ago, when the star of Venus could be seen,
I began to look at it through a telescope with great attention,
so that I might grasp with my physical senses an idea which I was
entertaining as certain. At first then you must know the planet
Venus appeared of a perfectly circular form, accurately so, and
bounded by a distinct edge, but very small; this figure Venus kept
until it began to approach its greatest distance from the sun,
and meanwhile the apparent size of its orb kept on increasing.
From that time it began to lose its roundness on the eastern side,
which was turned away from the sun, and in a few days it contracted
its visible portion into an exact semicircle; that figure lasted
without the smallest alteration until it began to return towards
the sun where it leaves the tangent drawn to its epicycle.[27]
At this time it loses the semicircular form more and more, and
keeps on diminishing that figure until its conjunction, when it
will wane to a very thin crescent. After completing its passage
past the sun, it will appear to us, at its appearance as a morning
star, as only sickle-shaped, turning a very thin crescent away from
the sun; afterwards the crescent will fill up more and more until
the planet reaches its greatest distance from the sun, in which
position it will appear semicircular, and that figure will last
for many days without appreciable variation. Then by degrees, from
being semicircular it will change to a full orb, and will keep that
perfectly circular figure for several months; but at this instant
the diameter of the orb of Venus is about five times as large as
that which it showed at its first appearance as an evening star.

“From the observation of these wonderful phenomena we are supplied
with a determination most conclusive, and appealing to the evidence
of our senses, of two very important problems, which up to this
day were discussed by the greatest intellects with different
conclusions. One is that the planets are bodies not self-luminous
(if we may entertain the same views about Mercury as we do about
Venus). The second is that we are absolutely compelled to say
that Venus (and Mercury also) revolves round the sun, as do also
all the rest of the planets. A truth believed indeed by the
Pythagorean school, by Copernicus, and by Kepler, but never proved
by the evidence of our senses, as it is now proved in the case of
Venus and Mercury. Kepler therefore and the rest of the school
of Copernicus have good reason for boasting that they have shown
themselves good philosophers, and that their belief was not devoid
of foundation; however much it has been their lot, and may even
hereafter be their lot, to be regarded by the philosophers of our
times, who philosophise on paper, with an universal agreement, as
men of no intellect, and little better than absolute fools.

“The words which I sent with their letters transposed, and which
said,

Haec immatura a me jam frustra leguntur, o.y.

when reduced to their proper order, read thus,

Cynthiae figuras aemulatur mater amorum:
The mother of the Loves rivals the phases of Cynthia:

that is,

Venus imitates the phases of the Moon.

“Three days ago I observed an eclipse of the moon, but not anything
worthy of special notice occurred in it. Only the edge of the
shadow appeared indistinct, blurred, and hazy; the cause of the
phenomenon no doubt is that the shadow has its origin at the earth,
at a great distance from the body of the moon.

“I have some other particulars, but I am prevented by time from
writing about them, etc.”

So writes Galileo.

[27] In the Ptolemaic system the earth’s centre was regarded as the
centre of the universe, and the movements of the heavenly bodies
were explained by eccentrics and epicycles. The sun was conceived
to describe a circle about a point not exactly coinciding with the
centre of the earth, called the sun’s _eccentric_. The planets
described epicycles (circles) whose centres described eccentrics
(circles), and the centres of these eccentrics coincided with the
centre of the sun’s eccentric. In the case of Mercury and Venus
the centre of the epicycle was always on the line drawn from the
centre of the eccentric to the sun’s centre. In the case of the
other planets the construction was more complicated. The stationary
points were determined by drawing tangents from the earth’s centre
(or the observer) to the epicycle, as in the figure (1).—(GASSENDI,
_Institutio Astronomica_, 1647.) This will explain Kepler’s
description of the stationary points as the points where the
planet leaves the tangent to its epicycle, supposing that he uses
the terms of the current (_i.e._ Ptolemaic) astronomy. Copernicus
placed the sun instead of the earth at the centre of the universe,
but to determine the positions of the planets at any given time
with as much accuracy as was attainable with the Ptolemaic system,
he was obliged to use a similar method of eccentrics and epicycles,
so that Kepler’s expression may be understood to describe the
stationary points according to the Copernican theory, though it
is still strange that he should not recognise the elliptical form
of the planetary orbits, which he had lately demonstrated after
most laborious reasoning in his _Commentaries on the Motion of the
Planet Mars_, 1609. Galileo’s own expression seems to describe the
stationary points according to the Copernican system, as would be
expected, as the points where the planet leaves the tangent drawn
to its _orbit_ from the earth (Fig. 2).

What now, dear reader, shall we make out of our telescope? Shall we make a Mercury’s magic-wand to cross the liquid ether with, and, like Lucian,[28] lead a colony to the uninhabited evening star, allured by the sweetness of the place? or shall we make it a Cupid’s arrow, which, entering by our eyes, has pierced our inmost mind, and fired us with a love of Venus? For what language is too strong for the marvellous beauty of this orb, if, having no light of its own, it can attain simply by the borrowed light of the sun to such splendour, as Jupiter has not, nor the moon, though enjoying a proximity to the sun as close as Venus; for if the moon’s light be compared with the light of Venus, it will be seen to be certainly greater on account of the apparent magnitude of the moon, but, in comparison with the light of Venus, dull, dead, and leaden. O truly golden Venus! Will any one doubt any more that the whole orb of Venus is wrought most smoothly out of pure unalloyed gold, since its surface, when only placed in the sunlight, reflects a splendour so intense! And here let me add my experiments about the alteration of the light of Venus on blinking the eye, which I have examined in the part of my Astronomy which treats of Optics. Reasoning will be able to conclude nothing else but this, that the orb of Venus turns on its own axis with an exceedingly swift rotation, displaying one after another different parts of its surface which are more or less capable of retaining the sun’s light.[29]

[28] Lucian, _Ver. Hist._ i. 12.

[29] The first scientific determination of the period of the
rotation of Venus was made by Dominique Cassini in 1666, from
observations of spots on the planet, and concluded to be about 24
hours; but in 1726 Bianchini deduced a period of 24 d. 8 h. from
similar observations. The true period is considered to be 23 h. 21
m., determined by Schroeter by a series of observations lasting
from 1788 to 1793 on the periodicity of the deformation of the
horns of Venus.—(ARAGO, _Astronomie Populaire_, 1854.)

Kepler’s statements can only be regarded as anticipations of
phenomena not yet actually observed.

But enough of my own conclusions. Let us now hear as an epilogue Galileo’s conclusions built up out of all the observations which he has made with his telescope, and announced from time to time. Thus he writes once more:—

[Sidenote: Galileo’s conclusions with regard to the inherent nature of the brightness of the stars.]

“Illustrissimo e Reverendissimo Signore mio colendissimo.

“Ho ricevuto gusto, e contento particolarissimo nella lettura
dell’ ultima di Vostra Signoria Illustrissima e Reverendissima
delli 7 stante, ed in particolare in quella parte dove ella
m’accenna la favorevole inclinazione dell’ Illustriss. Sig.
Cons. Wackher, verso di me, la quale io infinitamente stimo,
ed apprezzo; e poichè quella ha principalmente origine dall’
aver io incontrate osservazioni necessariamente dimostranti
conclusioni per avanti tenute vere da sua Signoria Illustrissima
per confermarmi maggiormente il possesso di grazia tanto pregiata
da me, prego Vostra Signoria Illustrissima e Reverendissima a
fargli intendere per mia parte come conforme alla credenza di
Sua Signoria Illustrissima ho dimostrazione certa, che siccome
tutti i Pianeti ricevono il lume dal Sole, essendo per se stessi
tenebrosi, e opachi; così le Stelle fisse risplendono per lor
natura, non bisognose dell’ illustrazione de’ raggi solari, li
quali, Dio sa, se arrivino a tanta altezza, più di quello, che
arrivi a noi il lume di una di esse fisse. Il principal fondamento
del mio discorso è nell’ osservare io molto evidentemente con
gli occhiali che quei Pianeti di mano in mano, che si trovano
più vicini a noi, o al Sole, ricevono maggiore splendore, e più
illustremente ce lo riverberano; e perciò Marte perigeo, e a noi
vicinissimo si vede assai più splendido, che Giove; benchè a
quello di mole assai inferiore; e difficilmente se gli può coll’
occhiale levare quella irradiazione, che impedisce il vedere il suo
disco terminato, e rotondo; il che in Giove non accade, vedendosi
esquisitamente circolare. Saturno poi per la sua gran lontananza
si vede esattamente terminato, sì la Stella maggiore di mezzo,
come le due piccole laterali; ed appare il suo lume languido, ed
abbacinato e senza niuna irradiazione, che impedisca il distinguere
i suoi tre piccoli globi terminatissimi. Ora poichè apertamente
veggiamo, che il Sole molto splendidamente illustra Marte vicino,
e che molto più languido è il lume di Giove (sebbene senza lo
strumento appare assai chiaro, il che accade per la grandezza, e
candore della Stella) languidissimo, e fosco quello di Saturno,
come molto più lontano, quali doveriano apparirci le Stelle
fisse lontane indicibilmente più di Saturno, quando il lume loro
derivasse dal Sole? Certamente debolissime, torbide e smorte. Ma
tutto l’opposito si vede, perocchè se rimireremo per esempio il
Cane, incontreremo un fulgore vivissimo, che quasi ci toglie la
vista, con una vibrazione di raggi tanto fiera, e possente, che
in comparazione di quello rimangono i Pianeti, e dico Giove e
Venere stessa, come un impurissimo vetro appresso un limpidissimo
e finissimo diamante. E benchè il disco di esso Cane apparisca non
maggiore della cinquantesima parte di quello di Giove, tuttavia la
sua irradiazione è grande, e fiera in modo, che l’istesso globo
tra i proprii crini s’implica, e quasi si perde, e con qualche
difficoltà si distingue; dove che Giove (e molto più Saturno)
si vedono e terminati, e di una luce languida, e per così dire
quieta. E per tanto io stimo, che bene filosoferemo, referendo la
causa della scintillazione delle Stelle fisse, al vibrare, che elle
fanno dello splendore proprio e nativo dall’intima loro sustanza;
dove che nella superficie de’ Pianeti termina più presto, e si
finisce l’illuminazione, che dal Sole deriva, e si parte. Se io
sentirò qualche particolare questione ricevuta dal medesimo Sig.
Wackher, non resterò d’affaticarmivi intorno, per dimostrarmi,
quale io sono desiderosissimo di servire un tanto Signore, e non
già con isperanza di aggiungere al termine conseguito dal suo
discorso, perchè benissimo comprendo, che a quanto sia passato
per lo finissimo cribro del giudizio di esso, e del Sig. Keplero,
non si può aggiungere di squisitezza; nè io pretenderei altro,
che col dubitare, e mal filosofare, eccitar loro al ritrovamento
di nuove sottigliezze. Gl’ingegni singolari, che in gran numero
fioriscono nell’Alemagna, mi hanno lungo tempo tenuto in desiderio
di vederla, il qual desiderio ora si raddoppia per la nuova grazia
dell’Illustrissimo Sig. Wackher, la quale mi farebbe divenir
grande ogni picciola occasione, che mi si presentasse. Ma ho di
soverchio occupata Vostra Signoria Illustrissima e Reverendissima.
Degnisi per fine di offerirmi e dedicarmi devotissimo servidore
all’Illustrissimo Sig. Wackher, salutando anco caramente il Sig.
Keplero, ed a lei con ogni riverenza bacio le mani, e dal Signore
Dio le prego somma felicità.

“[Di Firenze li 26] di Marzo 1611. Di Vostra Signoria Illustrissima
e Reverendissima obbligatissimo Servidore,

GALILEO GALILEI.”

When translated, the meaning is as follows:—

“Your last letter has exceedingly pleased me, especially that part
which assures me of the friendly feeling entertained towards me by
the most illustrious Imperial Counsellor, Wagher, which I for my
part highly appreciate. And since the cause of this friendliness
is, that I have incontestably demonstrated by some observations of
mine certain conclusions which he had long held as true, I wish
to confirm my possession of favour, which I value so much, and
accordingly I ask you to give him this piece of news from me; that
I have most conclusive arguments ready, showing clearly that, just
as he holds, all the planets receive their light from the sun,
being by constitution bodies dark and devoid of light;[30] but that
the fixed stars shine by their own proper light, not needing to be
illuminated by the sun’s rays, since God knows whether they reach
the very remote region of the fixed stars with intensity even equal
to the small intensity with which the rays of the fixed stars come
down to us.