Part 6

[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.

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.