# The Sidereal Messenger of Galileo Galilei/Kepler's Continuation

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.
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, 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?"
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.
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. 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
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.
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.
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 publicatiou of the new phenomena which any one had seen; he himself meanwhile described his discovery in letters transposed in this manner: smaismrmilmepoetaleumibunenugttauiras. Out of these ​letters I made an uncouth verse which I inserted in my Short Account in the month of September of last year:—
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:—
"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 Ilustrissima 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 . 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."
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,
"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, . 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 further 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
but where there is scarcely a chink of a nail's-breadth all round.
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.
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:—
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.
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, 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:—
"Illustrissimo e Reverendissimo Signore mio colendissimo.
"E 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 ​ E the Earth {centre of Universe). S the Sun. C centre of eccentric. D centre of planet's epicycle. V V′ stationary points. s v v′ projections of S V V on the ecliptic of which E′ is the center.
S the Sun, centre of solar system. v e positions of planet and earth at conjunction. V V′ stationary points of planet. E E′ corresponding positions of the Earth.
​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. Luna 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.
"Te 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 Ilustrissima 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 Ilustrissima 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. 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,
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.
​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, 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. •••••••• 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:—
Galileo's conclusions with regard to the inherent nature of the brightness of the stars."Illustrissimo e Reverendissimo Signore mio colendissimo.
"IIo 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. II 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; 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.
"My demonstration depends chiefly on this fact, that with the telescope I have distinctly observed that the planets receive greater brightness, and reflect it more intensely, in proportion as each one is nearer to us and to the sun. So Mars in perigee, that is, when nearest to the earth, greatly surpasses Jupiter in brightness, although in actual size it is far inferior to Jupiter; and in consequence it is difficult to receive the effulgence of this planet in the telescope, for it is so great as to prevent the eye from being able to distinguish the circular termination of the planet's disc. This does not happen in the case of Jupiter, for it appears quite circular. The next planet, Saturn, on account of its great distance likewise—for indeed it is the most remote of the planets,—appears bounded by a well-defined edge, both the greater orb in the middle and the two small orbs at its sides. Indeed, it appears to shine with a faint and delicate light, without any effulgence to prevent an observer recognising the well-defined termination of its three orbs. Since, then, we see that Mars, the nearest of the three, is illumined by the sun with very great splendour, and ​that the light of Jupiter, at a greater distance, is much more faint (although without the use of an instrument it appears tolerably bright, which is due to the size and brilliancy of its body), and that the light of Saturn, at the greatest distance, is most faint, and almost watery, of what kind, do you think, would appear the light of the fixed stars, which are at an immeasurable distance further from the sun than Saturn, if they only received light from the sun? Most certainly, extremely feeble, indistinct, and pallid. And yet we find quite the contrary; for, let us look with our eyes at the Dog-Star, for example. We shall encounter a most vivid brilliancy, which almost pricks the eye with the rapid sparkling of its rays, of such intensity that, in comparison with it, the planets, even Jupiter, and Venus too, are as thoroughly outshone as common and bad glass compared with a highly polished and most sparkling diamond. And although the orb of the Dog-Star appears no larger than the fiftieth part of Jupiter's disc, nevertheless its brilliancy is great and very strong; so that the form of its disc, which you expect to see, hides itself among the rays of its own refulgence, envelops itself in them, and almost disappears; and it is not distinguished without some difficulty from the rays which surround it. Whereas Jupiter, and still more Saturn, are seen well ​defined; and their light is without intensity, and, if I may say so, quiescent. Wherefore I think that we shall rightly apply our philosophy if we refer the cause of the twinkling of the fixed stars to vibrations of a brilliancy, which is their own, belonging to their constitution, and inherent in their substance, and say, on the other hand, that the illumination of the planets, which is derived from the sun, and distributed to the world, is limited to their surface."
These are the scientific conclusions in Galileo's letter; the rest I omit.
You see then, studious reader, how the subtle mind of Galileo, in my opinion the first philosopher of the day, uses this telescope of ours like a sort of ladder, scales the furthest and loftiest walls of the visible world, surveys all things with his own eyes, and, from the position he has gained, darts the glances of his most acute intellect upon these petty abodes of ours—the planetary spheres I mean,—and compares with keenest reasoning the distant with the near, the lofty with the deep.
VALE ET DEUM IN OPERIBUS SUIS CELEBRARE NUNQUAM DESINE.
Kepler, Narratio.
Edinburgh University Press: thomas and archibald constable, printers to her majesty.
* ↑ Diodorus Siculus, ii. 47.
* ↑ 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 eccentric 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 αἰτολογητός (Prague), 1609.
* ↑ 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. 6 h. 32 m.
* ↑ 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.
* ↑ 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.
* ↑ Virgil, Eclog. iii. 105.
* ↑ 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 farther 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.
* ↑ 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.)
* ↑ 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).
* ↑ Lucian, Ver. Hist. i. 12.
* ↑ 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 23h. 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.
* ↑ Proctor (Other Worlds than Ours, 1875) has given some reasons for believing that Jupiter and Saturn shine in part with their own light, owing to their great internal heat.
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