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.
[Illustration: Fig. 1.
_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._]
[Illustration: Fig. 2.
_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).