Title: The Sidereal Messenger of Galileo Galilei
 - and a Part of the Preface to Kepler's Dioptrics Containing the Original Account of Galileo's Astronomical Discoveries
Author: Galilei, Galileo, Kepler, Johannes
Language: English
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THE SIDEREAL MESSENGER


    RIVINGTONS

    London      _Waterloo Place_

    Oxford      _Magdalen Street_

    Cambridge   _Trinity Street_


[Illustration: GALILEO’S BROKEN LENS.

EXHIBITED IN THE LOAN COLLECTION OF SCIENTIFIC APPARATUS AT THE SOUTH
KENSINGTON MUSEUM, 1876.

_From a photograph of the Science and Art Department, South
Kensington._]



    THE SIDEREAL MESSENGER

    OF

    GALILEO GALILEI

    _AND A PART OF THE PREFACE TO KEPLER’S DIOPTRICS_

    CONTAINING THE ORIGINAL ACCOUNT OF GALILEO’S
    ASTRONOMICAL DISCOVERIES.

    A Translation with Introduction and Notes

    BY

    EDWARD STAFFORD CARLOS, M.A.

    HEAD MATHEMATICAL MASTER IN CHRIST’S HOSPITAL.

    RIVINGTONS
    _WATERLOO PLACE, LONDON_
    Oxford and Cambridge
    MDCCCLXXX



PREFATORY NOTE.


About five years ago I was engaged in preparing a catalogue of the
ancient books which belong to Christ’s Hospital. One portion of these
books consisted of a collection of ancient mathematical works presented
at various times for the use of that part of the school which is known
as the Royal Mathematical Foundation of King Charles II. Amongst
them were some well known by name to every mathematical student, but
which few have ever seen. Perhaps the most interesting of them all
was a little volume, printed in London in 1653, containing Gassendi’s
_Explanation of the Ptolemaic and Copernican Systems of Astronomy_, as
well as that of Tycho Brahe, Galileo’s _Sidereus Nuncius_, and Kepler’s
_Dioptrics_. I found Galileo’s account of his astronomical discoveries
so interesting, both in matter and in style, that I translated it as a
recreation from school-work. I venture to think that others also will
be interested in following Galileo through the apprehension of his
famous discoveries, and in reading the language in which he announced
them.



INTRODUCTION.


In 1609, Galileo, then Professor of Mathematics at Padua, in the
service of the Venetian Republic, heard from a correspondent at Paris
of the invention of a telescope, and set to work to consider how
such an instrument could be made. The result was his invention of
the telescope known by his name, and identical in principle with the
modern opera-glass. In a maritime and warlike State, the advantages
to be expected from such an invention were immediately recognised,
and Galileo was rewarded with a confirmation of his Professorship for
life, and a handsome stipend, in recognition of his invention and
construction of the first telescope seen at Venice. In his pamphlet,
_The Sidereal Messenger_, here translated, Galileo relates how he came
to learn the value of the telescope for astronomical research; and
how his observations were rewarded by numerous discoveries in rapid
succession, and at length by that of Jupiter’s satellites. Galileo at
once saw the value of this discovery as bearing upon the establishment
of the Copernican system of astronomy, which had met with slight
acceptance, and indeed as yet had hardly any recommendation except
that of greater simplicity. Kepler had just published at Prague his
work on the planet Mars (_Commentaria de motibus Stellæ Martis_),
on which he had been engaged apparently for eight years; there he
heard of Galileo’s discoveries, and at length was invited by Galileo
himself, through a common friend, Giuliano de’ Medici, ambassador of
the Grand-Duke of Tuscany, Cosmo de’ Medici II., to the Emperor Rudolph
II., to correspond with Galileo on the subject of these discoveries.
The Emperor also requested his opinion, and Kepler accordingly examined
Galileo’s _Sidereal Messenger_ in a pamphlet, entitled _A Discussion
with the Sidereal Messenger_ (Florence, 1610).

In this _Discussion_ Kepler gives reasons for accepting Galileo’s
observations—although he was not able to verify them from want of
a telescope—and entirely supports Galileo’s views and conclusions,
adducing his own previous speculations, or pointing out, as in the case
of Galileo’s idea of earth-light on the moon, the previous conception
of the same explanation of the phenomenon. He rejects, however,
Galileo’s explanation of the copper colour of the moon in eclipses.
Kepler ends by expressing unbounded enthusiasm at the discovery of
Jupiter’s satellites, and the argument it furnishes in support of the
Copernican theory.

Soon after, in 1611, Kepler published another pamphlet, his
_Narrative_, giving an account of actual observations made in
verification of Galileo’s discoveries by himself and several friends,
whose names he gives, with a telescope made by Galileo, and belonging
to Ernest, Elector and Archbishop of Cologne. Kepler and his friends
saw the lunar mountains and three of the satellites of Jupiter, but
failed to make out any signs of the ring of Saturn corresponding to the
imperfect description of Galileo.

Kepler had previously published a treatise on Optics (Frankfort, 1604).
He now extended it to the consideration of the theory of the telescope,
and explained the principle of Galileo’s telescope; he also showed
another combination of lenses which would produce a similar effect.
This was the principle of the common astronomical telescope, often
called, from this circumstance, Kepler’s telescope, though he did not
construct it. The account of Galileo’s later astronomical discoveries
of Saturn’s ring and the phases of Venus is taken from the preface of
this work.—(Kepler’s _Dioptrics_; Augsburg, 1611.)

In 1612 Galileo published a series of observations of solar spots, and
in 1618 some observations of three comets. There exist also long series
of minute observations of Jupiter and his satellites, continued to
November 1619.—(Galileo’s _Works_; Florence, 1845.)

Further astronomical researches may have been hindered by failing
sight. One more astronomical discovery, however, that of the moon’s
librations, was made as late as 1637, and the announcement of it is
dated “dalla mia carcere di Arcetri.” Galileo died January 8, 1642.


The following editions have been used for the translation:—

Galileo’s _Works_.

    1.  Florence, 1718.
    2.  Padua, 1744.
    3.  Florence, 1842-56.


_Sidereus Nuncius._

    1.  Venice, 1610.
    2.  London, 1653.


Kepler’s _Works_, ed. C. Frisch. Frankfurt a. M., 1858-71.

    Prodromus dissertationum mathematicarum continens Mysterium
    Cosmographicum de admirabili proportione orbium cœlestium.
    Tübingen, 1596.

    Astronomia nova αἰτιολογητός (Commentaria de motibus stellæ
    Martis). [Prague,] 1609.



    THE

    SIDEREAL MESSENGER

    OF

    GALILEO GALILEI



    THE

    SIDEREAL MESSENGER

    _UNFOLDING GREAT AND MARVELLOUS SIGHTS, AND PROPOSING THEM TO
    THE ATTENTION OF EVERY ONE, BUT ESPECIALLY PHILOSOPHERS AND
    ASTRONOMERS_,

    BEING SUCH AS HAVE BEEN OBSERVED BY

    GALILEO GALILEI

    A GENTLEMAN OF FLORENCE, PROFESSOR OF MATHEMATICS IN THE UNIVERSITY
    OF PADUA,

    WITH THE AID OF A

    TELESCOPE

    _lately invented by him_,

    _Respecting the Moon’s Surface, an innumerable number of Fixed
    Stars, the Milky Way, and Nebulous Stars, but especially respecting
    Four Planets which revolve round the Planet Jupiter at different
    distances and in different periodic times, with amazing velocity,
    and which, after remaining unknown to every one up to this day, the
    Author recently discovered, and determined to name the_

    MEDICEAN STARS.

    Venice 1610.


TO THE MOST SERENE

COSMO DE’ MEDICI, THE SECOND,

_FOURTH GRAND-DUKE OF TUSCANY_.


There is certainly something very noble and large-minded in the
intention of those who have endeavoured to protect from envy the noble
achievements of distinguished men, and to rescue their names, worthy
of immortality, from oblivion and decay. This desire has given us
the lineaments of famous men, sculptured in marble, or fashioned in
bronze, as a memorial of them to future ages; to the same feeling we
owe the erection of statues, both ordinary and equestrian; hence, as
the poet[1] says, has originated expenditure, mounting to the stars,
upon columns and pyramids; with this desire, lastly, cities have been
built, and distinguished by the names of those men, whom the gratitude
of posterity thought worthy of being handed down to all ages. For the
state of the human mind is such, that unless it be continually stirred
by the counterparts[2] of matters, obtruding themselves upon it from
without, all recollection of the matters easily passes away from it.

    [1] Propertius, iii. 2. 17-22.

    [2] Compare Lucretius iv. 881:

    Dico animo nostro primum simulacra meandi Accidere, atque animum
    pulsare.

But others, having regard for more stable and more lasting monuments,
secured the eternity of the fame of great men by placing it under the
protection, not of marble or bronze, but of the Muses’ guardianship
and the imperishable monuments of literature. But why do I mention
these things, as if human wit, content with these regions, did not
dare to advance further; whereas, since she well understood that all
human monuments do perish at last by violence, by weather, or by age,
she took a wider view, and invented more imperishable signs, over
which destroying Time and envious Age could claim no rights; so,
betaking herself to the sky, she inscribed on the well-known orbs of
the brightest stars—those everlasting orbs—the names of those who, for
eminent and god-like deeds, were accounted worthy to enjoy an eternity
in company with the stars. Wherefore the fame of Jupiter, Mars,
Mercury, Hercules, and the rest of the heroes by whose names the stars
are called, will not fade until the extinction of the splendour of the
constellations themselves.

But this invention of human shrewdness, so particularly noble and
admirable, has gone out of date ages ago, inasmuch as primeval heroes
are in possession of those bright abodes, and keep them by a sort of
right; into whose company the affection of Augustus in vain attempted
to introduce Julius Cæsar; for when he wished that the name of the
Julian constellation should be given to a star, which appeared in
his time, one of those which the Greeks and the Latins alike name,
from their hair-like tails, comets, it vanished in a short time and
mocked his too eager hope. But we are able to read the heavens for
your highness, most Serene Prince, far more truly and more happily,
for scarcely have the immortal graces of your mind begun to shine
on earth, when bright stars present themselves in the heavens, like
tongues to tell and celebrate your most surpassing virtues to all
time. Behold therefore, four stars reserved for your famous name, and
those not belonging to the common and less conspicuous multitude of
fixed stars, but in the bright ranks of the planets—four stars which,
moving differently from each other, round the planet Jupiter, the
most glorious of all the planets, as if they were his own children,
accomplish the courses of their orbits with marvellous velocity,
while all the while with one accord they complete all together mighty
revolutions every ten years round the centre of the universe, that is,
round the Sun.

But the Maker of the Stars himself seemed to direct me by clear reasons
to assign these new planets to the famous name of your highness in
preference to all others. For just as these stars, like children worthy
of their sire, never leave the side of Jupiter by any appreciable
distance, so who does not know that clemency, kindness of heart,
gentleness of manners, splendour of royal blood, nobleness in public
functions, wide extent of influence and power over others, all of which
have fixed their common abode and seat in your highness,—who, I say,
does not know that all these qualities, according to the providence of
God, from whom all good things do come, emanate from the benign star
of Jupiter? Jupiter, Jupiter, I maintain, at the instant of the birth
of your highness having at length emerged from the turbid mists of the
horizon, and being in possession of the middle quarter of the heavens,
and illuminating the eastern angle, from his own royal house, from
that exalted throne, looked out upon your most happy birth, and poured
forth into a most pure atmosphere all the brightness of his majesty,
in order that your tender body and your mind—though that was already
adorned by God with still more splendid graces—might imbibe with your
first breath the whole of that influence and power. But why should I
use only plausible arguments when I can almost absolutely demonstrate
my conclusion? It was the will of Almighty God that I should be judged
by your most serene parents not unworthy to be employed in teaching
your highness mathematics, which duty I discharged, during the four
years just passed, at that time of the year when it is customary to
take a relaxation from severer studies. Wherefore, since it evidently
fell to my lot by God’s will, to serve your highness, and so to receive
the rays of your surpassing clemency and beneficence in a position near
your person, what wonder is it if you have so warmed my heart that
it thinks about scarcely anything else day and night, but how I, who
am indeed your subject not only by inclination, but also by my very
birth and lineage, may be known to be most anxious for your glory, and
most grateful to you? And so, inasmuch as under your patronage, most
serene Cosmo, I have discovered these stars, which were unknown to
all astronomers before me, I have, with very good right, determined
to designate them with the most august name of your family. And as I
was the first to investigate them, who can rightly blame me if I give
them a name, and call them _the Medicean Stars_, hoping that as much
consideration may accrue to these stars from this title, as other stars
have brought to other heroes? For not to speak of your most serene
ancestors, to whose everlasting glory the monuments of all history bear
witness, your virtue alone, most mighty sire, can confer on those stars
an immortal name; for who can doubt that you will not only maintain and
preserve the expectations, high though they be, about yourself, which
you have aroused by the very happy beginning of your government, but
that you will also far surpass them, so that when you have conquered
others like yourself, you may still vie with yourself, and become day
by day greater than yourself and your greatness?

Accept, then, most clement Prince, this addition to the glory of your
family, reserved by the stars for you; and may you enjoy for many years
those good blessings, which are sent to you not so much from the stars
as from God, the Maker and Governor of the stars.

    Your Highness’s most devoted servant,

    Galileo Galilei.

    Padua, _March 12, 1610_.



THE ASTRONOMICAL MESSENGER


    _Containing and setting forth Observations lately made with the aid
    of a newly invented_ Telescope _respecting the Moon’s Surface, the
    Milky Way, Nebulous Stars, an innumerable multitude of Fixed Stars,
    and also respecting Four Planets never before seen, which have been
    named_

    THE COSMIAN STARS.[3]

    [3] The satellites of Jupiter are here called “_the Cosmian Stars_”
    in honour of Cosmo de’ Medici, but elsewhere Galileo calls them
    “_the Medicean Stars_.” Kepler sometimes calls them “_the Medicean
    Stars_,” but more often “_satellites_.”

[Sidenote: Introduction.]

IN the present small treatise I set forth some matters of great
interest for all observers of natural phenomena to look at and
consider. They are of great interest, I think, first, from their
intrinsic excellence; secondly, from their absolute novelty; and
lastly, also on account of the instrument by the aid of which they have
been presented to my apprehension.

The number of the Fixed Stars which observers have been able to see
without artificial powers of sight up to this day can be counted. It is
therefore decidedly a great feat to add to their number, and to set
distinctly before the eyes other stars in myriads, which have never
been seen before, and which surpass the old, previously known, stars in
number more than ten times.

Again, it is a most beautiful and delightful sight to behold the body
of the Moon, which is distant from us nearly sixty _semi_-diameters[4]
of the Earth, as near as if it was at a distance of only two of the
same measures; so that the diameter of this same Moon appears about
thirty times larger, its surface about nine hundred times, and its
solid mass nearly 27,000 times larger than when it is viewed only with
the naked eye; and consequently any one may know with the certainty
that is due to the use of our senses, that the Moon certainly does not
possess a smooth and polished surface, but one rough and uneven, and,
just like the face of the Earth itself, is everywhere full of vast
protuberances, deep chasms, and sinuosities.

    [4] Galileo says, “per sex denas fere terrestres _diametros_ a
    nobis remotum” by mistake for _semi-diametros_, and the same
    mistake occurs in p. 11.

Then to have got rid of disputes about the Galaxy or Milky Way, and
to have made its nature clear to the very senses, not to say to the
understanding, seems by no means a matter which ought to be considered
of slight importance. In addition to this, to point out, as with one’s
finger, the nature of those stars which every one of the astronomers
up to this time has called _nebulous_, and to demonstrate that it is
very different from what has hitherto been believed, will be pleasant,
and very fine. But that which will excite the greatest astonishment by
far, and which indeed especially moved me to call the attention of all
astronomers and philosophers, is this, namely, that I have discovered
four planets, neither known nor observed by any one of the astronomers
before my time, which have their orbits round a certain bright star,
one of those previously known, like Venus and Mercury round the Sun,
and are sometimes in front of it, sometimes behind it, though they
never depart from it beyond certain limits. All which facts were
discovered and observed a few days ago by the help of a telescope[5]
devised by me, through God’s grace first enlightening my mind.

    [5] The words used by Galileo for “telescope” are _perspicillum_,
    _specillum instrumentum_, _organum_, and _occhiale_ (Ital.).
    Kepler uses also _oculare tubus_, _arundo dioptrica_. The word
    “_telescopium_” is used by Gassendi, 1647.

Perchance other discoveries still more excellent will be made from time
to time by me or by other observers, with the assistance of a similar
instrument, so I will first briefly record its shape and preparation,
as well as the occasion of its being devised, and then I will give an
account of the observations made by me.

[Sidenote: Galileo’s account of the invention of his telescope.]

About ten months ago a report reached my ears that a Dutchman had
constructed a telescope, by the aid of which visible objects, although
at a great distance from the eye of the observer, were seen distinctly
as if near; and some proofs of its most wonderful performances were
reported, which some gave credence to, but others contradicted. A few
days after, I received confirmation of the report in a letter written
from Paris by a noble Frenchman, Jaques Badovere, which finally
determined me to give myself up first to inquire into the principle of
the telescope, and then to consider the means by which I might compass
the invention of a similar instrument, which a little while after I
succeeded in doing, through deep study of the theory of Refraction;
and I prepared a tube, at first of lead, in the ends of which I fitted
two glass lenses, both plane on one side, but on the other side one
spherically convex, and the other concave. Then bringing my eye to the
concave lens I saw objects satisfactorily large and near, for they
appeared one-third of the distance off and nine times larger than
when they are seen with the natural eye alone. I shortly afterwards
constructed another telescope with more nicety, which magnified
objects more than sixty times. At length, by sparing neither labour
nor expense, I succeeded in constructing for myself an instrument
so superior that objects seen through it appear magnified nearly a
thousand times, and more than thirty times nearer than if viewed by the
natural powers of sight alone.

[Sidenote: Galileo’s first observations with his telescope.]

It would be altogether a waste of time to enumerate the number and
importance of the benefits which this instrument may be expected to
confer, when used by land or sea. But without paying attention to its
use for terrestrial objects, I betook myself to observations of the
heavenly bodies; and first of all, I viewed the Moon as near as if it
was scarcely two _semi_-diameters[6] of the Earth distant. After the
Moon, I frequently observed other heavenly bodies, both fixed stars
and planets, with incredible delight; and, when I saw their very great
number, I began to consider about a method by which I might be able to
measure their distances apart, and at length I found one. And here it
is fitting that all who intend to turn their attention to observations
of this kind should receive certain cautions. For, in the first
place, it is absolutely necessary for them to prepare a most perfect
telescope, one which will show very bright objects distinct and free
from any mistiness, and will magnify them at least 400 times, for then
it will show them as if only one-twentieth of their distance off. For
unless the instrument be of such power, it will be in vain to attempt
to view all the things which have been seen by me in the heavens, or
which will be enumerated hereafter.

    [6] “Vix per duas Telluris _diametros_,” by mistake for
    “semi-diametros.”

[Sidenote: Method of determining the magnifying power of the telescope.]

But in order that any one may be a little more certain about the
magnifying power of his instrument, he shall fashion two circles, or
two square pieces of paper, one of which is 400 times greater than the
other, but that will be when the diameter of the greater is twenty
times the length of the diameter of the other. Then he shall view from
a distance simultaneously both surfaces, fixed on the same wall, the
smaller with one eye applied to the telescope, and the larger with the
other eye unassisted; for that may be done without inconvenience at one
and the same instant with both eyes open. Then both figures will appear
of the same size, if the instrument magnifies objects in the desired
proportion.

[Sidenote: Method of measuring small angular distances between heavenly
bodies by the size of the aperture of the telescope.]

After such an instrument has been prepared, the method of measuring
distances remains for inquiry, and this we shall accomplish by the
following contrivance:—

[Illustration]

For the sake of being more easily understood, I will suppose a tube A
B C D.[7] Let E be the eye of the observer; then, when there are no
lenses in the tube rays from the eye to the object F G would be drawn
in the straight lines E C F, E D G, but when the lenses have been
inserted, let the rays go in the bent lines E C H, E D I,—for they are
contracted, and those which originally, when unaffected by the lenses,
were directed to the object F G, will include only the part H I. Hence
the ratio of the distance E H to the line H I being known, we shall
be able to find, by means of a table of sines, the magnitude of the
angle subtended at the eye by the object H I, which we shall find to
contain only some minutes. But if we fit on the lens C D thin plates
of metal, pierced, some with larger, others with smaller apertures, by
putting on over the lens sometimes one plate, sometimes another, as may
be necessary, we shall construct at our pleasure different subtending
angles of more or fewer minutes, by the help of which we shall be
able to measure conveniently the intervals between stars separated by
an angular distance of some minutes, within an error of one or two
minutes. But let it suffice for the present to have thus slightly
touched, and as it were just put our lips to these matters, for on
some other opportunity I will publish the theory of this instrument in
completeness.

    [7] [Illustration]

    The line C H in Galileo’s figure represents the small pencil of
    rays from H which, after refraction through the telescope, reach
    the eye E. The enlarged figure shows that if O P be the radius of
    the aperture employed, the point H of the object would be just
    outside the field of view. The method, however, is at best only
    a very rough one, as the boundary of the field of view in this
    telescope is unavoidably indistinct.

Now let me review the observations made by me during the two months
just past, again inviting the attention of all who are eager for true
philosophy to the beginnings which led to the sight of most important
phenomena.

[Sidenote: The Moon. Ruggedness of its surface. Existence of lunar
mountains and valleys.]

Let me speak first of the surface of the Moon, which is turned towards
us. For the sake of being understood more easily, I distinguish two
parts in it, which I call respectively the brighter and the darker. The
brighter part seems to surround and pervade the whole hemisphere; but
the darker part, like a sort of cloud, discolours the Moon’s surface
and makes it appear covered with spots. Now these spots, as they
are somewhat dark and of considerable size, are plain to every one,
and every age has seen them, wherefore I shall call them _great_ or
_ancient_ spots, to distinguish them from other spots, smaller in size,
but so thickly scattered that they sprinkle the whole surface of the
Moon, but especially the brighter portion of it. These spots have never
been observed by any one before me; and from my observations of them,
often repeated, I have been led to that opinion which I have expressed,
namely, that I feel sure that the surface of the Moon is not perfectly
smooth, free from inequalities and exactly spherical, as a large
school of philosophers considers with regard to the Moon and the other
heavenly bodies, but that, on the contrary, it is full of inequalities,
uneven, full of hollows and protuberances, just like the surface of the
Earth itself, which is varied everywhere by lofty mountains and deep
valleys.

Sketches by Galileo to shew:—

[Illustration: the indentation of the terminator and illuminated
summits of mountains in the dark part of the moon;]

[Illustration: the shape of a lunar mountain and of a walled plain.
Galileo: ‘Sidereus Nuncius,’ Venice 1610.]

The appearances from which we may gather these conclusions are of the
following nature:—On the fourth or fifth day after new-moon, when
the Moon presents itself to us with bright horns, the boundary which
divides the part in shadow from the enlightened part does not extend
continuously in an ellipse, as would happen in the case of a perfectly
spherical body, but it is marked out by an irregular, uneven, and very
wavy line, as represented in the figure given, for several bright
excrescences, as they may be called, extend beyond the boundary of
light and shadow into the dark part, and on the other hand pieces of
shadow encroach upon the light:—nay, even a great quantity of small
blackish spots, altogether separated from the dark part, sprinkle
everywhere almost the whole space which is at the time flooded with the
Sun’s light, with the exception of that part alone which is occupied by
the great and ancient spots. I have noticed that the small spots just
mentioned have this common characteristic always and in every case,
that they have the dark part towards the Sun’s position, and on the
side away from the Sun they have brighter boundaries, as if they were
crowned with shining summits. Now we have an appearance quite similar
on the Earth about sunrise, when we behold the valleys, not yet flooded
with light, but the mountains surrounding them on the side opposite to
the Sun already ablaze with the splendour of his beams; and just as
the shadows in the hollows of the Earth diminish in size as the Sun
rises higher, so also these spots on the Moon lose their blackness
as the illuminated part grows larger and larger. Again, not only are
the boundaries of light and shadow in the Moon seen to be uneven
and sinuous, but—and this produces still greater astonishment—there
appear very many bright points within the darkened portion of the
Moon, altogether divided and broken off from the illuminated tract,
and separated from it by no inconsiderable interval, which, after a
little while, gradually increase in size and brightness, and after
an hour or two become joined on to the rest of the bright portion,
now become somewhat larger; but in the meantime others, one here and
another there, shooting up as if growing, are lighted up within the
shaded portion, increase in size, and at last are linked on to the
same luminous surface, now still more extended. An example of this
is given in the same figure. Now, is it not the case on the Earth
before sunrise, that while the level plain is still in shadow, the
peaks of the most lofty mountains are illuminated by the Sun’s rays?
After a little while does not the light spread further, while the
middle and larger parts of those mountains are becoming illuminated;
and at length, when the Sun has risen, do not the illuminated parts
of the plains and hills join together? The grandeur, however, of
such prominences and depressions in the Moon seems to surpass both
in magnitude and extent the ruggedness of the Earth’s surface, as I
shall hereafter show. And here I cannot refrain from mentioning what a
remarkable spectacle I observed while the Moon was rapidly approaching
her first quarter, a representation of which is given in the same
illustration, placed opposite page 16. A protuberance of the shadow, of
great size, indented the illuminated part in the neighbourhood of the
lower cusp; and when I had observed this indentation longer, and had
seen that it was dark throughout, at length, after about two hours, a
bright peak began to arise a little below the middle of the depression;
this by degrees increased, and presented a triangular shape, but was
as yet quite detached and separated from the illuminated surface. Soon
around it three other small points began to shine, until, when the Moon
was just about to set, that triangular figure, having now extended and
widened, began to be connected with the rest of the illuminated part,
and, still girt with the three bright peaks already mentioned, suddenly
burst into the indentation of shadow like a vast promontory of light.

At the ends of the upper and lower cusps also certain bright points,
quite away from the rest of the bright part, began to rise out of the
shadow, as is seen depicted in the same illustration.

[Sidenote: The lunar spots are suggested to be possibly seas bordered
by ranges of mountains.]

In both horns also, but especially in the lower one, there was a great
quantity of dark spots, of which those which are nearer the boundary
of light and shadow appear larger and darker, but those which are more
remote less dark and more indistinct. In all cases, however, just as I
have mentioned before, the dark portion of the spot faces the position
of the Sun’s illumination, and a brighter edge surrounds the darkened
spot on the side away from the Sun, and towards the region of the Moon
in shadow. This part of the surface of the Moon, where it is marked
with spots like a peacock’s tail with its azure eyes, is rendered like
those glass vases which, through being plunged while still hot from the
kiln into cold water, acquire a crackled and wavy surface, from which
circumstance they are commonly called _frosted glasses_.[8] Now the
great spots of the Moon observed at the same time are not seen to be
at all similarly broken, or full of depressions and prominences, but
rather to be even and uniform; for only here and there some spaces,
rather brighter than the rest, crop up; so that if any one wishes to
revive the old opinion of the Pythagoreans, that the Moon is another
Earth, so to say, the brighter portion may very fitly represent the
surface of the land, and the darker the expanse of water. Indeed, I
have never doubted that if the sphere of the Earth were seen from a
distance, when flooded with the Sun’s rays, that part of the surface
which is land would present itself to view as brighter, and that which
is water as darker in comparison. Moreover, the great spots in the
Moon are seen to be more depressed than the brighter tracts; for in
the Moon, both when crescent and when waning, on the boundary between
the light and shadow, which projects in some places round the great
spots, the adjacent regions are always brighter, as I have noticed in
drawing my illustrations, and the edges of the spots referred to are
not only more depressed than the brighter parts, but are more even,
and are not broken by ridges or ruggednesses. But the brighter part
stands out most near the spots, so that both before the first quarter
and about the third quarter also, around a certain spot in the upper
part of the figure, that is, occupying the northern region of the Moon,
some vast prominences on the upper and lower sides of it rise to an
enormous elevation, as the illustrations show. This same spot before
the third quarter is seen to be walled round with boundaries of a
deeper shade, which just like very lofty mountain summits appear darker
on the side away from the Sun, and brighter on the side where they face
the Sun; but in the case of the cavities the opposite happens, for the
part of them away from the Sun appears brilliant, and that part which
lies nearer to the Sun dark and in shadow. After a time, when the
enlightened portion of the Moon’s surface has diminished in size, as
soon as the whole or nearly so of the spot already mentioned is covered
with shadow, the brighter ridges of the mountains mount high above the
shade. These two appearances are shown in the illustrations which are
given.

    [8] Specimens of _frosted or crackled Venetian glass_ are to be
    seen in the Slade Collection, British Museum, and fully justify
    Galileo’s comparison.

[Sidenote: Description of a lunar crater, perhaps Tycho.][9]

    [9] Webb, _Celestial Objects for Common Telescopes_, p. 104,
    suggests this identification.


There is one other point which I must on no account forget, which I
have noticed and rather wondered at. It is this:—The middle of the
Moon, as it seems, is occupied by a certain cavity larger than all the
rest, and in shape perfectly round. I have looked at this depression
near both the first and third quarters, and I have represented it as
well as I can in the second illustration already given. It produces
the same appearance as to effects of light and shade as a tract like
Bohemia would produce on the Earth, if it were shut in on all sides by
very lofty mountains arranged on the circumference of a perfect circle;
for the tract in the Moon is walled in with peaks of such enormous
height that the furthest side adjacent to the dark portion of the
Moon is seen bathed in sunlight before the boundary between light and
shade reaches half-way across the circular space. But according to the
characteristic property of the rest of the spots, the shaded portion of
this too faces the Sun, and the bright part is towards the dark side of
the Moon, which for the third time I advise to be carefully noticed as
a most solid proof of the ruggednesses and unevennesses spread over the
whole of the bright region of the Moon. Of these spots, moreover, the
darkest are always those which are near to the boundary-line between
the light and the shadow, but those further off appear both smaller
in size and less decidedly dark; so that at length, when the Moon at
opposition becomes full, the darkness of the cavities differs from the
brightness of the prominences with a subdued and very slight difference.

[Sidenote: Reasons for believing that there is a difference of
constitution in various parts of the Moon’s surface.]

These phenomena which we have reviewed are observed in the bright
tracts of the Moon. In the great spots we do not see such differences
of depressions and prominences as we are compelled to recognise in the
brighter parts, owing to the change of their shapes under different
degrees of illumination by the Sun’s rays according to the manifold
variety of the Sun’s position with regard to the Moon. Still, in the
great spots there do exist some spaces rather less dark than the rest,
as I have noted in the illustrations, but these spaces always have the
same appearance, and the depth of their shadow is neither intensified
nor diminished; they do appear indeed sometimes a little more shaded,
sometimes a little less, but the change of colour is very slight,
according as the Sun’s rays fall upon them more or less obliquely;
and besides, they are joined to the adjacent parts of the spots with
a very gradual connection, so that their boundaries mingle and melt
into the surrounding region. But it is quite different with the spots
which occupy the brighter parts of the Moon’s surface, for, just as
if they were precipitous crags with numerous rugged and jagged peaks,
they have well-defined boundaries through the sharp contrast of light
and shade. Moreover, inside those great spots certain other tracts are
seen brighter than the surrounding region, and some of them very bright
indeed, but the appearance of these, as well as of the darker parts,
is always the same; there is no change of shape or brightness or depth
of shadow, so that it becomes a matter of certainty and beyond doubt
that their appearance is owing to real dissimilarity of parts, and
not to unevennesses only in their configuration, changing in different
ways the shadows of the same parts according to the variations of their
illumination by the Sun, which really happens in the case of the other
smaller spots occupying the brighter portion of the Moon, for day by
day they change, increase, decrease, or disappear, inasmuch as they
derive their origin only from the shadows of prominences.

[Sidenote: Explanation of the evenness of the illuminated part of
the circumference of the Moon’s orb by the analogy of terrestrial
phenomena, or by a possible lunar atmosphere.]

But here I feel that some people may be troubled with grave doubt, and
perhaps seized with a difficulty so serious as to compel them to feel
uncertain about the conclusion just explained and supported by so many
phenomena. For if that part of the Moon’s surface which reflects the
Sun’s rays most brightly is full of sinuosities, protuberances, and
cavities innumerable, why, when the Moon is increasing, does the outer
edge which looks toward the west, when the Moon is waning, the other
half-circumference towards the east, and at full-moon the whole circle,
appear not uneven, rugged, and irregular, but perfectly round and
circular, as sharply defined as if marked out with a pair of compasses,
and without the indentations of any protuberances or cavities? And most
remarkably so, because the whole unbroken edge belongs to that part of
the Moon’s surface which possesses the property of appearing brighter
than the rest, which I have said to be throughout full of protuberances
and cavities. For not one of the Great Spots extends quite to the
circumference, but all of them are seen to be together away from the
edge. Of this phenomenon, which affords a handle for such serious
doubt, I produce two causes, and so two solutions of the difficulty.

The first solution which I offer is this:—If the protuberances and
cavities in the body of the Moon existed only on the edge of the
circle that bounds the hemisphere which we see, then the Moon might,
or rather must, show itself to us with the appearance of a toothed
wheel, being bounded with an irregular and uneven circumference; but
if, instead of a single set of prominences arranged along the actual
circumference only, very many ranges of mountains with their cavities
and ruggednesses are set one behind the other along the extreme edge
of the Moon, and that too not only in the hemisphere which we see, but
also in that which is turned away from us, but still near the boundary
of the hemisphere, then the eye, viewing them afar off, will not at
all be able to detect the differences of prominences and cavities, for
the intervals between the mountains situated in the same circle, or in
the same chain, are hidden by the jutting forward of other prominences
situated in other ranges, and especially if the eye of the observer
is placed in the same line with the tops of the prominences mentioned.
So on the Earth, the summits of a number of mountains close together
appear situated in one plane, if the spectator is a long way off and
standing at the same elevation. So when the sea is rough, the tops of
the waves seem to form one plane, although between the billows there is
many a gulf and chasm, so deep that not only the hulls, but even the
bulwarks, masts, and sails of stately ships are hidden amongst them.
Therefore, as within the Moon, as well as round her circumference,
there is a manifold arrangement of prominences and cavities, and the
eye, regarding them from a great distance, is placed in nearly the
same plane with their summits, no one need think it strange that they
present themselves to the visual ray which just grazes them as an
unbroken line quite free from unevennesses. To this explanation may be
added another, namely, that there is round the body of the Moon, just
as round the Earth, an envelope of some substance denser than the rest
of the ether, which is sufficient to receive and reflect the Sun’s
rays, although it does not possess so much opaqueness as to be able to
prevent our seeing through it—especially when it is not illuminated.
That envelope, when illuminated by the Sun’s rays, renders the body
of the Moon apparently larger than it really is, and would be able
to stop our sight from penetrating to the solid body of the Moon, if
its thickness were greater; now, it is of greater thickness about the
circumference of the Moon, greater, I mean, not in actual thickness,
but with reference to our sight-rays, which cut it obliquely; and so it
may stop our vision, especially when it is in a state of brightness,
and may conceal the true circumference of the Moon on the side towards
the Sun.

[Illustration]

This may be understood more clearly from the adjoining figure, in which
the body of the Moon, A B C, is surrounded by an enveloping atmosphere,
D E G. An eye at F penetrates to the middle parts of the Moon, as
at A, through a thickness, D A, of the atmosphere; but towards the
extreme parts a mass of atmosphere of greater depth, E B, shuts out its
boundary from our sight. An argument in favour of this is, that the
illuminated portion of the Moon appears of larger circumference than
the rest of the orb which is in shadow.

Perhaps also some will think that this same cause affords a very
reasonable explanation why the greater spots on the Moon are not seen
to reach to the edge of the circumference on any side, although it
might be expected that some would be found about the edge as well as
elsewhere; and it seems credible that there are spots there, but that
they cannot be seen because they are hidden by a mass of atmosphere too
thick and too bright for the sight to penetrate.

[Illustration]

[Sidenote: Calculation to show that the height of some lunar mountains
exceeds four Italian miles[10] (22,000 British feet).]

    [10] In the list of the heights of lunar mountains determined by
    Beer and Maedler, given in their work _Der Mond_ (Berlin, 1837),
    there are six which exceed 3000 toises, or 19,000 British feet.

I think that it has been sufficiently made clear, from the explanation
of phenomena which have been given, that the brighter part of the
Moon’s surface is dotted everywhere with protuberances and cavities;
it only remains for me to speak about their size, and to show that the
ruggednesses of the Earth’s surface are far smaller than those of the
Moon’s; smaller, I mean, absolutely, so to say, and not only smaller
in proportion to the size of the orbs on which they are. And this is
plainly shown thus:—As I often observed in various positions of the
Moon with reference to the Sun, that some summits within the portion
of the Moon in shadow appeared illumined, although at some distance
from the boundary of the light (the terminator), by comparing their
distance with the complete diameter of the Moon, I learnt that it
sometimes exceeded the one-twentieth (1/20th) part of the diameter.
Suppose the distance to be exactly 1/20th part of the diameter, and
let the diagram represent the Moon’s orb, of which C A F is a great
circle, E its centre, and C F a diameter, which consequently bears
to the diameter of the Earth the ratio 2:7; and since the diameter
of the Earth, according to the most exact observations, contains
7000 Italian miles, C F will be 2000, and C E 1000, and the 1/20th
part of the whole, C F, 100 miles. Also let C F be a diameter of the
great circle which divides the bright part of the Moon from the dark
part (for, owing to the very great distance of the Sun from the Moon
this circle does not differ sensibly from a great one), and let the
distance of A from the point C be 1/20th part of that diameter; let
the radius E A be drawn, and let it be produced to cut the tangent
line G C D, which represents the ray that illumines the summit, in
the point D. Then the arc C A or the straight line C D will be 100 of
such units, as C E contains 1000. The sum of the squares of D C, C E is
therefore 1,010,000, and the square of D E is equal to this; therefore
the whole E D will be more than 1004; and A D will be more than 4 of
such units, as C E contained 1000. Therefore the height of A D in the
Moon, which represents a summit reaching up to the Sun’s ray, G C D,
and separated from the extremity C by the distance C D, is more than
4 Italian miles; but in the Earth there are no mountains which reach
to the perpendicular height even of one mile. We are therefore left to
conclude that it is clear that the prominences of the Moon are loftier
than those of the Earth.

[Sidenote: The faint illumination of the Moon’s disc about new-moon
explained to be due to earth-light.]

I wish in this place to assign the cause of another lunar phenomenon
well worthy of notice, and although this phenomenon was observed by me
not lately, but many years ago, and has been pointed out to some of my
intimate friends and pupils, explained, and assigned to its true cause,
yet as the observation of it is rendered easier and more vivid by the
help of a telescope, I have considered that it would not be unsuitably
introduced in this place, but I wish to introduce it chiefly in order
that the connection and resemblance between the Moon and the Earth may
appear more plainly.

When the Moon, both before and after conjunction, is found not far
from the Sun, not only does its orb show itself to our sight on the
side where it is furnished with shining horns, but a slight and faint
circumference is also seen to mark out the circle of the dark part,
that part, namely, which is turned away from the Sun, and to separate
it from the darker background of the sky. But if we examine the matter
more closely, we shall see that not only is the extreme edge of the
part in shadow shining with a faint brightness, but that the entire
face of the Moon, that side, that is, which does not feel the Sun’s
glare, is illuminated with a pale light of considerable brightness.
At the first glance only a fine circumference appears shining, on
account of the darker part of the sky adjacent to it; whereas, on the
contrary, the rest of the surface appears dark, on account of the
contiguity of the shining horns, which destroys the clearness of our
sight. But if any one chooses such a position for himself, that by the
interposition of a roof, or a chimney, or some other object between
his sight and the Moon, but at a considerable distance from his eye,
the shining horns are hidden, and the rest of the Moon’s orb is left
exposed to his view, then he will find that this tract of the Moon
also, although deprived of sunlight, gleams with considerable light,
and particularly so if the gloom of the night has already deepened
through the absence of the Sun; for with a darker background the same
light appears brighter. Moreover, it is found that this secondary
brightness of the Moon, as I may call it, is greater in proportion as
the Moon is less distant from the Sun; for it abates more and more in
proportion to the Moon’s distance from that body, so much so that after
the first quarter, and before the end of the second, it is found to be
weak and very faint, although it be observed in a darker sky; whereas,
at an angular distance of 60° or less, even during twilight, it is
wonderfully bright, so bright indeed that, with the help of a good
telescope, the great spots may be distinguished in it.

This strange brightness has afforded no small perplexity to
philosophical minds; and some have published one thing, some another,
as the cause to be alleged for it. Some have said that it is the
inherent and natural brightness of the Moon; some that it is imparted
to that body by the planet Venus; or, as others maintain, by all
the stars; while some have said that it comes from the Sun, whose
rays, they say, find a way through the solid mass of the Moon. But
statements of this kind are disproved without much difficulty, and
convincingly demonstrated to be false. For if this kind of light were
the Moon’s own, or were contributed by the stars, the Moon would retain
it, particularly in eclipses, and would show it then, when left in
an unusually dark sky, but this is contrary to experience. For the
brightness which is seen on the Moon in eclipses is far less intense,
being somewhat reddish, and almost copper-coloured, whereas this is
brighter and whiter; besides, the brightness seen during an eclipse is
changeable and shifting, for it wanders over the face of the Moon, so
that that part which is near the circumference of the circle of shadow
thrown by the Earth is bright, but the rest of the Moon is always seen
to be dark. From which circumstance we understand without hesitation
that this brightness is due to the proximity of the Sun’s rays coming
into contact with some denser region which surrounds the Moon as an
envelope; owing to which contact a sort of dawn-light is diffused over
the neighbouring regions of the Moon, just as the twilight spreads in
the morning and evening on the Earth:[11] but I will treat more fully
of this matter in my book upon the _System of the Universe_.[12]

    [11] The illumination of the Moon in eclipses, noticed by Galileo,
    is now referred to the refraction of the sunlight by the earth’s
    atmosphere, and the reddish colour of the light is explained by
    Herschel (_Outlines of Astronomy_, ch. vii.) to be due to the
    absorption of the violet and blue rays by the aqueous vapour of the
    Earth’s atmosphere. The idea of a sensible lunar atmosphere is not
    in accordance with the observed phenomena of the occultations of
    stars.

    [12] Galileo’s _Systema Mundi_. Owing to the violent opposition
    provoked by the discussion of the discoveries of Galileo, and
    their bearing on the Copernican system of astronomy, Galileo seems
    to have found it necessary to delay the publication of this work
    until 1632, when, believing himself safe under the friendship and
    patronage of Pope Urban VIII. and others in power at Rome, he
    at length published it. Urban, however, now turned against him,
    denounced the book and its author, and summoned him to Rome, where
    the well-known incidents of his trial and condemnation took place.

Again, to assert that this sort of light is imparted to the Moon by the
planet Venus is so childish as to be undeserving of an answer; for who
is so ignorant as not to understand that at conjunction and within an
angular distance of 60° it is quite impossible for the part of the Moon
turned away from the Sun to be seen by the planet Venus?

But that this light is derived from the Sun penetrating with its light
the solid mass of the Moon, and rendering it luminous, is equally
untenable. For then this light would never lessen, since the hemisphere
of the Moon is always illumined by the Sun, except at the moment of
a lunar eclipse, yet really it quickly decreases while the Moon is
drawing near to the end of her first quarter, and when she has passed
her first quarter it becomes quite dull. Since, therefore, this
kind of secondary brightness is not inherent and the Moon’s own, nor
borrowed from any of the stars, nor from the Sun, and since there now
remains in the whole universe no other body whatever except the Earth,
what, pray, must we conclude? What must we assert? Shall we assert that
the body of the Moon, or some other dark and sunless orb, receives
light from the Earth? Why should it not be the Moon? And most certainly
it is. The Earth, with fair and grateful exchange, pays back to the
Moon an illumination like that which it receives from the Moon nearly
the whole time during the darkest gloom of night. Let me explain the
matter more clearly. At conjunction, when the Moon occupies a position
between the Sun and the Earth, the Moon is illuminated by the Sun’s
rays on her half towards the Sun which is turned away from the Earth,
and the other half, with which she regards the Earth, is covered with
darkness, and so in no degree illumines the Earth’s surface. When the
Moon has slightly separated from the Sun, straightway she is partly
illumined on the half directed towards us; she turns towards us a
slender silvery crescent, and slightly illumines the Earth; the Sun’s
illumination increases upon the Moon as she approaches her first
quarter, and the reflexion of that light increases on the Earth; the
brightness in the Moon next extends beyond the semicircle, and our
nights grow brighter; at length the entire face of the Moon looking
towards the Earth is irradiated with the most intense brightness by
the Sun, which happens when the Sun and Moon are on opposite sides of
the Earth; then far and wide the surface of the Earth shines with the
flood of moonlight; after this the Moon, now waning, sends out less
powerful beams, and the Earth is illumined less powerfully; at length
the Moon draws near her first position of conjunction with the Sun, and
forthwith black night invades the Earth. In such a cycle the moonlight
gives us each month alternations of brighter and fainter illumination.
But the benefit of her light to the Earth is balanced and repaid by the
benefit of the light of the Earth to her; for while the Moon is found
near the Sun about the time of conjunction, she has in front of her
the entire surface of that hemisphere of the Earth which is exposed to
the Sun, and vividly illumined with his beams, and so receives light
reflected from the Earth. Owing to such reflexion, the hemisphere
of the Moon nearer to us, though deprived of sunlight, appears of
considerable brightness. Again, when removed from the Sun through
a quadrant, the Moon sees only one-half of the Earth’s hemisphere
illuminated, namely the western half, for the other, the eastern, is
covered with the shades of night; the Moon is, therefore, less brightly
enlightened by the Earth, and accordingly that secondary light appears
fainter to us. But if you imagine the Moon to be set on the opposite
side of the Earth to the Sun, she will see the hemisphere of the Earth,
now between the Moon and the Sun, quite dark, and steeped in the gloom
of night; if, therefore, an eclipse should accompany such a position
of the Moon, she will receive no light at all, being deprived of the
illumination of the Sun and Earth together. In any other position, with
regard to the Earth and the Sun, the Moon receives more or less light
by reflexion from the Earth, according as she sees a greater or smaller
portion of the hemisphere of the Earth illuminated by the Sun; for such
a law is observed between these two orbs, that at whatever times the
Earth is most brightly enlightened by the Moon, at those times, on the
contrary, the Moon is least enlightened by the Earth; and contrariwise.
Let these few words on this subject suffice in this place; for I will
consider it more fully in my _System of the Universe_, where, by very
many arguments and experimental proofs, there is shown to be a very
strong reflexion of the Sun’s light from the Earth, for the benefit of
those who urge that the Earth must be separated from the starry host,
chiefly for the reason that it has neither motion nor light, for I will
prove that the Earth has motion, and surpasses the Moon in brightness,
and is not the place where the dull refuse of the universe has settled
down; and I will support my demonstration by a thousand arguments taken
from natural phenomena.

[Sidenote: Stars. Their appearance in the telescope.]

Hitherto I have spoken of the observations which I have made concerning
the Moon’s body; now I will briefly announce the phenomena which have
been, as yet, seen by me with reference to the Fixed Stars. And first
of all the following fact is worthy of consideration:—The stars, fixed
as well as erratic, when seen with a telescope, by no means appear to
be increased in magnitude in the same proportion as other objects,
and the Moon herself, gain increase of size; but in the case of the
stars such increase appears much less, so that you may consider that
a telescope, which (for the sake of illustration) is powerful enough
to magnify other objects a hundred times, will scarcely render the
stars magnified four or five times. But the reason of this is as
follows:—When stars are viewed with our natural eyesight they do not
present themselves to us of their bare, real size, but beaming with a
certain vividness, and fringed with sparkling rays, especially when
the night is far advanced; and from this circumstance they appear much
larger than they would if they were stripped of those adventitious
fringes, for the angle which they subtend at the eye is determined
not by the primary disc of the star, but by the brightness which so
widely surrounds it. Perhaps you will understand this most clearly
from the well-known circumstance that when stars rise just at sunset,
in the beginning of twilight, they appear very small, although they
may be stars of the first magnitude; and even the planet Venus itself,
on any occasion when it may present itself to view in broad daylight,
is so small to see that it scarcely seems to equal a star of the last
magnitude. It is different in the case of other objects, and even of
the Moon, which, whether viewed in the light of midday or in the depth
of night, always appears of the same size. We conclude therefore that
the stars are seen at midnight in uncurtailed glory, but their fringes
are of such a nature that the daylight can cut them off, and not only
daylight, but any slight cloud which may be interposed between a star
and the eye of the observer. A dark veil or coloured glass has the
same effect, for, upon placing them before the eye between it and
the stars, all the blaze that surrounds them leaves them at once. A
telescope also accomplishes the same result, for it removes from the
stars their adventitious and accidental splendours before it enlarges
their true discs (if indeed they are of that shape), and so they seem
less magnified than other objects, for a star of the fifth or sixth
magnitude seen through a telescope is shown as of the first magnitude
only.

The difference between the appearance of the planets and the fixed
stars seems also deserving of notice. The planets present their discs
perfectly round, just as if described with a pair of compasses,
and appear as so many little moons, completely illuminated and of
a globular shape; but the fixed stars do not look to the naked eye
bounded by a circular circumference, but rather like blazes of
light, shooting out beams on all sides and very sparkling, and with
a telescope they appear of the same shape as when they are viewed by
simply looking at them, but so much larger that a star of the fifth or
sixth magnitude seems to equal Sirius, the largest of all the fixed
stars.[13]

    [13] The immense distance of stars makes it impossible for them to
    be magnified by any telescope, however powerful; the apparent or
    spurious disc is an optical effect, which depends on the telescope
    used, and is smallest with the largest aperture.

[Illustration: _Orion’s Belt and Sword; 83 Stars_]

[Illustration: _Pleiades; 36 Stars_

_Galileo: “Sidereus Nuncius.”_]

[Sidenote: Telescopic Stars: their infinite multitude. As examples,
Orion’s Belt and Sword and the Pleiades are described as seen by
Galileo.]

But beyond the stars of the sixth magnitude you will behold through
the telescope a host of other stars, which escape the unassisted
sight, so numerous as to be almost beyond belief, for you may see more
than six other differences of magnitude, and the largest of these,
which I may call stars of the seventh magnitude, or of the first
magnitude of invisible stars, appear with the aid of the telescope
larger and brighter than stars of the second magnitude seen with the
unassisted sight. But in order that you may see one or two proofs of
the inconceivable manner in which they are crowded together, I have
determined to make out a case against two star-clusters, that from them
as a specimen you may decide about the rest.

As my first example I had determined to depict the entire constellation
of Orion, but I was overwhelmed by the vast quantity of stars and
by want of time, and so I have deferred attempting this to another
occasion, for there are adjacent to, or scattered among, the old stars
more than five hundred new stars within the limits of one or two
degrees. For this reason I have selected the three stars in Orion’s
Belt and the six in his Sword, which have been long well-known groups,
and I have added eighty other stars recently discovered in their
vicinity, and I have preserved as exactly as possible the intervals
between them. The well-known or old stars, for the sake of distinction,
I have depicted of larger size, and I have outlined them with a double
line; the others, invisible to the naked eye, I have marked smaller and
with one line only. I have also preserved the differences of magnitude
as much as I could.

As a second example I have depicted the six stars of the constellation
Taurus, called the Pleiades (I say _six_ intentionally, since the
seventh is scarcely ever visible), a group of stars which is enclosed
in the heavens within very narrow precincts. Near these there lie
more than forty others invisible to the naked eye, no one of which is
much more than half a degree off any of the aforesaid six; of these
I have noticed only thirty-six in my diagram. I have preserved their
intervals, magnitudes, and the distinction between the old and the new
stars, just as in the case of the constellation Orion.

[Sidenote: The Milky Way consists entirely of stars in countless
numbers and of various magnitudes.]

The next object which I have observed is the essence or substance of
the Milky Way. By the aid of a telescope any one may behold this in a
manner which so distinctly appeals to the senses that all the disputes
which have tormented philosophers through so many ages are exploded at
once by the irrefragable evidence of our eyes, and we are freed from
wordy disputes upon this subject, for the Galaxy is nothing else but a
mass of innumerable stars planted together in clusters. Upon whatever
part of it you direct the telescope straightway a vast crowd of
stars presents itself to view; many of them are tolerably large
and extremely bright, but the number of small ones is quite beyond
determination.

[Illustration: _Star-cluster in Orion’s Head_]

[Illustration: _Star-cluster of Praesepe in Cancer_

_Galileo: “Sidereus Nuncius,” Venice, 1610._]

[Sidenote: Nebulæ resolved into clusters of stars: as examples, the
nebulæ in Orion’s Head and Præsepe.]

And whereas that milky brightness, like the brightness of a white
cloud, is not only to be seen in the Milky Way, but several spots of
a similar colour shine faintly here and there in the heavens, if you
turn the telescope upon any of them you will find a cluster of stars
packed close together. Further—and you will be more surprised at
this,—the stars which have been called by every one of the astronomers
up to this day _nebulous_, are groups of small stars set thick together
in a wonderful way, and although each one of them on account of its
smallness, or its immense distance from us, escapes our sight, from
the commingling of their rays there arises that brightness which has
hitherto been believed to be the denser part of the heavens, able to
reflect the rays of the stars or the Sun.

I have observed some of these, and I wish to subjoin the star-clusters
of two of these nebulæ. First, you have a diagram of the nebula called
that of Orion’s Head, in which I have counted twenty-one stars.

The second cluster contains the nebula called Præsepe, which is not one
star only, but a mass of more than forty small stars. I have noticed
thirty-six stars, besides the Aselli, arranged in the order of the
accompanying diagram.

[Sidenote: Discovery of Jupiter’s satellites, Jan. 7, 1610: record of
Galileo’s observations during two months.]

I have now finished my brief account of the observations which I have
thus far made with regard to the Moon, the Fixed Stars, and the Galaxy.
There remains the matter, which seems to me to deserve to be considered
the most important in this work, namely, that I should disclose and
publish to the world the occasion of discovering and observing four
PLANETS, never seen from the very beginning of the world up to our
own times, their positions, and the observations made during the last
two months about their movements and their changes of magnitude; and
I summon all astronomers to apply themselves to examine and determine
their periodic times, which it has not been permitted me to achieve up
to this day, owing to the restriction of my time. I give them warning
however again, so that they may not approach such an inquiry to no
purpose, that they will want a very accurate telescope, and such as I
have described in the beginning of this account.

On the 7th day of January in the present year, 1610, in the first[14]
hour of the following night, when I was viewing the constellations of
the heavens through a telescope, the planet Jupiter presented itself to
my view, and as I had prepared for myself a very excellent instrument,
I noticed a circumstance which I had never been able to notice before,
owing to want of power in my other telescope, namely, that three little
stars, small but very bright, were near the planet; and although I
believed them to belong to the number of the fixed stars, yet they made
me somewhat wonder, because they seemed to be arranged exactly in a
straight line, parallel to the ecliptic,[15] and to be brighter than
the rest of the stars, equal to them in magnitude. The position of them
with reference to one another and to Jupiter was as follows (Fig. 1).

    [14] The times of Galileo’s observations are to be understood as
    reckoned from sunset.

    [15] The satellites of Jupiter revolve in planes very nearly,
    although not exactly, coincident with that of the equator of the
    planet, which is inclined 3° 5´ 30´´ to the orbit of the planet,
    and the plane of the orbit is inclined 1° 18´ 51´´ to the ecliptic.

On the east side there were two stars, and a single one towards the
west. The star which was furthest towards the east, and the western
star, appeared rather larger than the third.

I scarcely troubled at all about the distance between them and Jupiter,
for, as I have already said, at first I believed them to be fixed
stars; but when on January 8th, led by some fatality, I turned again to
look at the same part of the heavens, I found a very different state
of things, for there were three little stars all west of Jupiter, and
nearer together than on the previous night, and they were separated
from one another by equal intervals, as the accompanying illustration
(Fig. 2) shows.

At this point, although I had not turned my thoughts at all upon the
approximation of the stars to one another, yet my surprise began to
be excited, how Jupiter could one day be found to the east of all the
aforesaid fixed stars when the day before it had been west of two of
them; and forthwith I became afraid lest the planet might have moved
differently from the calculation of astronomers, and so had passed
those stars by its own proper motion. I therefore waited for the next
night with the most intense longing, but I was disappointed of my hope,
for the sky was covered with clouds in every direction.

But on January 10th the stars appeared in the following position with
regard to Jupiter; there were two only, and both on the east side of
Jupiter, the third, as I thought, being hidden by the planet (Fig. 3).
They were situated just as before, exactly in the same straight line
with Jupiter, and along the Zodiac.

When I had seen these phenomena, as I knew that corresponding
changes of position could not by any means belong to Jupiter, and as,
moreover, I perceived that the stars which I saw had been always the
same, for there were no others either in front or behind, within a
great distance, along the Zodiac,—at length, changing from doubt into
surprise, I discovered that the interchange of position which I saw
belonged not to Jupiter, but to the stars to which my attention had
been drawn, and I thought therefore that they ought to be observed
henceforward with more attention and precision.

Accordingly, on January 11th I saw an arrangement of the following
kind (Fig. 4), namely, only two stars to the east of Jupiter, the
nearer of which was distant from Jupiter three times as far as from
the star further to the east; and the star furthest to the east was
nearly twice as large as the other one; whereas on the previous night
they had appeared nearly of equal magnitude. I therefore concluded,
and decided unhesitatingly, that there are three stars in the heavens
moving about Jupiter, as Venus and Mercury round the Sun; which
at length was established as clear as daylight by numerous other
subsequent observations. These observations also established that there
are not only three, but four, erratic sidereal bodies performing their
revolutions round Jupiter, observations of whose changes of position
made with more exactness on succeeding nights the following account
will supply. I have measured also the intervals between them with the
telescope in the manner already explained. Besides this, I have given
the times of observation, especially when several were made in the
same night, for the revolutions of these planets are so swift that an
observer may generally get differences of position every hour.

Jan. 12.—At the first hour of the next night I saw these heavenly
bodies arranged in this manner (Fig. 5). The satellite[16] furthest to
the east was greater than the satellite furthest to the west; but both
were very conspicuous and bright; the distance of each one from Jupiter
was two minutes. A third satellite, certainly not in view before, began
to appear at the third hour; it nearly touched Jupiter on the east
side, and was exceedingly small. They were all arranged in the same
straight line, along the ecliptic.

    [16] Galileo continues to call these bodies _stars_, perhaps
    meaning “Medicean stars,” throughout the description of their
    configurations, but as he had now detected their nature, it is more
    convenient to call them _satellites_, the term introduced by Kepler.

Jan. 13.—For the first time four satellites were in view in the
following position with regard to Jupiter (Fig. 6).

There were three to the west, and one to the east; they made a straight
line nearly, but the middle satellite of those to the west deviated a
little from the straight line towards the north. The satellite furthest
to the east was at a distance of 2´ from Jupiter; there were intervals
of 1´ only between Jupiter and the nearest satellite, and between the
satellites themselves, west of Jupiter. All the satellites appeared
of the same size, and though small they were very brilliant, and far
outshone the fixed stars of the same magnitude.

Jan. 14.—The weather was cloudy.

Jan. 15.—At the third hour of the night the four satellites were in the
state depicted in the next diagram (Fig. 7) with reference to Jupiter.

All were to the west, and arranged nearly in the same straight line;
but the satellite which counted third from Jupiter was raised a little
to the north. The nearest to Jupiter was the smallest of all; the
rest appeared larger and in order of magnitude; the intervals between
Jupiter and the three nearest satellites were all equal, and were of
the magnitude of 2´ each; but the satellite furthest to the west was
distant 4´ from the satellite nearest to it. They were very brilliant,
and not at all twinkling, as they have always appeared both before
and since. But at the seventh hour there were only three satellites,
presenting with Jupiter an appearance of the following kind (Fig. 8).
They were, that is to say, in the same straight line to a hair; the
nearest to Jupiter was very small, and distant from the planet 3´; the
distance of the second from this one was 1´; and of the third from the
second 4´ 30´´. But after another hour the two middle satellites were
still nearer, for they were only 30´´, or less, apart.

Jan. 16.—At the first hour of the night I saw three satellites arranged
in this order (Fig. 9). Jupiter was between two of them, which were at
a distance of 0´ 40´´ from the planet on either side, and the third was
west of Jupiter at a distance of 8´. The satellites near to Jupiter
appeared brighter than the satellite further off, but not larger.

Jan. 17, after sunset 0 hours 30 minutes, the configuration was of
this kind (Fig. 10). There was one satellite only to the east, at a
distance of 3´ from Jupiter; to the west likewise there was only one
satellite, distant 11´ from Jupiter. The satellite on the east appeared
twice as large as the satellite to the west; and there were no more
than these two. But four hours after, that is, nearly at the fifth
hour, a third satellite began to emerge on the east side, which, before
its appearance, as I think, had been joined with the former of the two
other satellites, and the position was of this kind (Fig. 11). The
middle satellite was very near indeed to the satellite on the east,
and was only 20´´ from it; and was a little towards the south of the
straight line drawn through the two extreme satellites and Jupiter.

Jan. 18, at 0 h. 20 m. after sunset, the appearance was such as this
(Fig. 12). The satellite to the east was larger than the western one,
and was at a distance from Jupiter of 8´, the western one being at a
distance of 10´.

Jan. 19.—At the second hour of the night the relative position of
the satellites was such as this (Fig. 13); that is, there were three
satellites exactly in a straight line with Jupiter, one to the east, at
a distance of 6´ from Jupiter; between Jupiter and the first satellite
to the west in order, there was an interval of 5´; this satellite was
4´ off the other one more to the west. At that time I was doubtful
whether or no there was a satellite between the satellite to the east
and Jupiter, but so very close to Jupiter as almost to touch the
planet; but at the fifth hour I saw this satellite distinctly, by
that time occupying exactly the middle position between Jupiter and
the eastern satellite, so that the configuration was thus (Fig. 14).
Moreover, the satellite which had just come into view was very small;
yet at the sixth hour it was nearly as large as the rest.

Jan. 20: 1 h. 15 m.—A similar arrangement was seen (Fig. 15). There
were three satellites, so small as scarcely to be distinguishable;
their distances from Jupiter, and from one another, were not more
than 1´. I was doubtful whether on the western side there were two
satellites or three. About the sixth hour they were grouped in this way
(Fig. 16). The eastern satellite was twice as far away from Jupiter as
before, that is 2´; on the western side, the satellite in the middle
was distant from Jupiter 0´ 40´´, and from the satellite still further
to the west 0´ 20´´; at length, at the seventh hour, three satellites
were seen on the western side (Fig. 17). The satellite nearest to
Jupiter was distant from the planet 0´ 20´´; between this one and the
satellite furthest to the west there was an interval of 40´´, but
between these another satellite was in view slightly southward of them,
and not more than 10´´ off the most westerly satellite.

Jan. 21: 0 h. 30 m.—There were three satellites on the east side; the
satellites and Jupiter were at equal distances apart (Fig. 18). The
intervals were by estimation 50´´ each. There was also one satellite
on the west, distant 4´ from Jupiter. The satellite on the east side
nearest to Jupiter was the least of all.

Jan. 22: 2 h.—The grouping of the satellites was similar (Fig. 19).
There was an interval of 5´ from the satellite on the east to Jupiter;
from Jupiter to the satellite furthest to the west 7´. The two interior
satellites on the western side were 0´ 40´´ apart, and the satellite
nearer to Jupiter was 1´ from the planet. The inner satellites were
smaller than the outer ones, but they were situated all in the same
straight line, along the ecliptic, except that the middle of the
three western satellites was slightly to the south of it, but at the
sixth hour of the night they appeared in this position (Fig. 20). The
satellite on the east was very small, at a distance from Jupiter of 5´
as before; but the three satellites on the west were separated by equal
distances from Jupiter and from each other; and the intervals were
nearly 1´ 20´´ each. The satellite nearest Jupiter appeared smaller
than the other two on the same side, but they all appeared arranged
exactly in the same straight line.

Jan. 23, at 0 h. 40 m. after sunset, the grouping of the satellites
was nearly after this fashion (Fig. 21). There were three satellites
with Jupiter in a straight line along the ecliptic, as they always
have been; two were on the east of the planet, one on the west; the
satellite furthest to the east was 7´ from the next one, and this
satellite 2´ 40´´ from Jupiter; Jupiter was 3´ 20´´ from the satellite
on the west; and they were all of nearly the same size. But at the
fifth hour the two satellites which had been previously near Jupiter
were no longer visible, being, as I suppose, hidden behind Jupiter, and
the appearance presented was such as this (Fig. 22).

Jan. 24.—Three satellites, all on the east side, were visible, and
nearly, but not quite, in the same straight line with Jupiter, for the
satellite in the middle was slightly to the south of it (Fig. 23). The
satellite nearest to Jupiter was 2´ distant from the planet; the next
in order 0´ 30´´ from this satellite, and the third was 9´ further off
still; they were all very bright. But at the sixth hour two satellites
only presented themselves to view in this position, namely in the same
straight line with Jupiter exactly, and the distance of the nearest
to the planet was lengthened to 3´; the next was 2´ further off, and
unless I am mistaken, the two satellites previously observed in the
middle had come together, and appeared as one.

Jan. 25, at 1 h. 40 m., the satellites were grouped thus (Fig. 24).
There were only two satellites on the east side, and these were rather
large. The satellite furthest to the east was 5´ from the satellite in
the middle, and it was 6´ from Jupiter.

Jan. 26, at 0 h. 40 m., the relative positions of the satellites were
thus (Fig. 25). Three satellites were in view, of which two were
east and the third west of Jupiter; this one was distant 3´ from the
planet. On the east side the satellite in the middle was at a distance
of 5´ 20´´; the further satellite was 6´ beyond; they were arranged
in a straight line, and were of the same size. At the fifth hour the
arrangement was nearly the same, with this difference only, that the
fourth satellite was emerging on the east side near Jupiter. It was
smaller than the rest, and was then at a distance of 0´ 30´´ from
Jupiter; but was raised a little above the straight line towards the
north, as the accompanying figure shows (Fig. 26).

Jan. 27, 1 h. after sunset, a single satellite only was in view, and
that on the east side of Jupiter in this position (Fig. 27). It was
very small, and at a distance of 7´ from Jupiter.

Jan. 28 and 29.—Owing to the intervention of clouds, I could make no
observation.

Jan. 30.—At the first hour of the night the satellites were in view,
arranged in the following way (Fig. 28). There was one satellite on
the east side, at a distance of 2´ 30´´ from Jupiter; and there were
two satellites on the west, of which the one nearer to Jupiter was
3´ off the planet, and the other satellite 1´ further. The places of
the outer satellites and Jupiter were in the same straight line; but
the satellite in the middle was a little above it to the north. The
satellite furthest to the west was smaller than the rest.

On the last day of the month, at the second hour, two satellites on
the east side were visible, and one on the west (Fig. 29). Of the
satellites east of the planet, the one in the middle was 2´ 20´´
distant from Jupiter; and the satellite further to the east was 0´ 30´´
from the middle satellite; the satellite on the west was at a distance
of 10´ from Jupiter. They were in the same straight line nearly, and
would have been exactly so, only the satellite on the east nearest to
Jupiter was raised a little towards the north. At the fourth hour, the
two satellites on the east were still nearer together, for they were
only 20´´ apart (Fig. 30). The western satellite appeared rather small
in these two observations.

Feb. 1.—At the second hour of the night the arrangement was similar
(Fig. 31). The satellite furthest to the east was at a distance of 6´
from Jupiter, and the western satellite 8´. On the east side there was
a very small satellite, at a distance of 20´´ from Jupiter. They made a
perfectly straight line.

Feb. 2.—The satellites were seen arranged thus (Fig. 32). There was one
only on the east, at a distance of 6´ from Jupiter. Jupiter was 4´
from the nearest satellite on the west; between this satellite and the
satellite further to the west there was an interval of 8´; they were in
the same straight line exactly, and were nearly of the same magnitude.
But at the seventh hour four satellites were there—two on each side
of Jupiter (Fig. 33). Of these satellites, the most easterly was at a
distance of 4´ from the next; this satellite was 1´ 40´´ from Jupiter;
Jupiter was 6´ from the nearest satellite on the west, and this one
from the satellite further to the west, 8´; and they were all alike in
the same straight line, drawn in the direction of the Zodiac.

Feb. 3: 7 h.—The satellites were arranged in the following way (Fig.
34):—The satellite on the east was at a distance of 1´ 30´´ from
Jupiter; the nearest satellite on the west, 2´, and there was a
long distance, 10´, from this satellite to the satellite further to
the west. They were exactly in the same straight line, and of equal
magnitude.

Feb. 4: 2 h.—Four satellites attended Jupiter, two on the east and
two on the west, arranged in one perfectly straight line, as in the
adjoining figure (Fig. 35). The satellite furthest to the east was at
a distance of 3´ from the next satellite. This one was 0´ 40´´ from
Jupiter; Jupiter 4´ from the nearest satellite on the west; and this
one from the satellite further to the west 6´. In magnitude they were
nearly equal; the satellite nearest to Jupiter was rather smaller in
appearance than the rest. But at the seventh hour (Fig. 36) the eastern
satellites were at a distance of only 0´ 30´´ apart. Jupiter was 2´
from the nearest satellite on the east; and from the satellite on the
west, next in order, 4´; this one was distant 3´ from the satellite
further to the west. They were all equal in magnitude, and in a
straight line, drawn in the direction of the ecliptic.

Feb. 5.—The sky was cloudy.

Feb. 6.—Two satellites only appeared, with Jupiter between them, as is
seen in the accompanying figure (Fig. 37). The satellite on the east
was 2´ from Jupiter, and that on the west 3´. They were in the same
straight line with Jupiter, and were equal in magnitude.

Feb. 7.—There were two satellites by the side of Jupiter, and both of
them on the east of the planet, arranged in this manner (Fig. 38).
The intervals between the satellites and Jupiter were equal, and of
1´ each; and a straight line would go through them and the centre of
Jupiter.

Feb. 8: 1 h.—Three satellites were there, all on the east side of
Jupiter, as in the diagram (Fig. 39). The nearest to Jupiter, a
rather small one, was distant from the planet 1´ 20´´; the middle
one was 4´ from this satellite, and was rather large; the satellite
furthest to the east, a very small one, was at a distance of 0´ 20´´
from this satellite. It was doubtful whether there was one satellite
near to Jupiter or two, for sometimes it seemed that there was another
satellite by its side towards the east, wonderfully small, and only
10´´ from it. They were all situated at points in a straight line drawn
in the direction of the Zodiac. At the third hour the satellite nearest
to Jupiter was almost touching the planet, for it was only distant
10´´ from it; but the others had become further off, for the middle
one was 6´ from Jupiter. At length, at the fourth hour, the satellite
which was previously the nearest to Jupiter joined with the planet and
disappeared.

Feb. 9: 0 h. 30 m.—There were two satellites on the east side of
Jupiter, and one on the west, in an arrangement such as this (Fig. 40).
The satellite furthest to the east, which was a rather small one, was
distant 4´ from the next satellite; the satellite in the middle was
larger, and at a distance of 7´ from Jupiter. Jupiter was distant 4´
from the western satellite, which was a small one.

Feb. 10: 1 h. 30 m.—A pair of satellites, very small, and both on the
east of the planet, were visible, in the following position (Fig. 41).
The further satellite was distant from Jupiter 10´, the nearer 0´ 20´´,
and they were in the same straight line; but at the fourth hour the
satellite nearest to Jupiter no longer appeared, and the other seemed
so diminished that it could scarcely be kept in sight, although the
atmosphere was quite clear, and the satellite was further from Jupiter
than before, since its distance was now 12´.

Feb. 11: 1 h.—There were two satellites on the east, and one on the
west (Fig. 42). The western satellite was at a distance of 4´ from
Jupiter. The satellite on the east, nearest to the planet, was likewise
4´ from Jupiter; but the satellite further to the east was at a
distance from this one of 8´; they were fairly clear to view, and in
the same straight line; but at the third hour the fourth satellite was
visible near to Jupiter on the east, less in magnitude than the rest,
separated from Jupiter by a distance of 0´ 30´´, and slightly to the
north out of the straight line drawn through the rest (Fig. 43). They
were all very bright and extremely distinct, but at 5 h. 30 m. the
satellite on the east nearest to Jupiter had moved further away from
the planet, and was occupying a position midway between the planet and
the neighbouring satellite further to the east. They were all in the
same straight line exactly, and of the same magnitude, as may be seen
in the accompanying diagram (Fig. 44).

Feb. 12: 0 h. 40 m.—A pair of satellites on the east, a pair likewise
on the west, were near the planet (Fig. 45). The satellite on the
east furthest removed from Jupiter was at a distance of 10´, and the
further of the satellites on the west was 8´ off. They were both fairly
distinct. The other two were very near to Jupiter, and very small,
especially the satellite to the east, which was at a distance of 0´
40´´ from Jupiter. The distance of the western satellite was 1´. But at
the fourth hour the satellite which was nearest to Jupiter on the east
was visible no longer.

Feb. 13: 0 h. 30 m.—Two satellites were visible in the east, two also
in the west (Fig. 46). The satellite on the east near Jupiter was
fairly distinct; its distance from the planet was 2´. The satellite
further to the east was less noticeable; it was distant 4´ from the
other. Of the satellites on the west, the one furthest from Jupiter,
which was very distinct, was parted from the planet 4´. Between this
satellite and Jupiter intervened a small satellite close to the most
westerly satellite, being not more than 0´ 3´´ off. They were all in
the same straight line, corresponding exactly to the direction of the
ecliptic.

Feb. 15 (for on the 14th the sky was covered with clouds), at the
first hour, the position of the satellites was thus (Fig. 47); that
is, there were three satellites on the east, but none were visible
on the west. The satellite on the east nearest to Jupiter was at a
distance of 0´ 50´´ from the planet; the next in order was 0´ 20´´
from this satellite, and the furthest to the east was 2´ from the
second satellite, and it was larger than the others, for those nearer
to Jupiter were very small. But about the fifth hour only one of the
satellites which had been near to Jupiter was to be seen; its distance
from Jupiter was 0´ 30´´. The distance of the satellite furthest to the
east from Jupiter had increased, for it was then 4´ (Fig. 48). But at
the sixth hour, besides the two situated as just described on the east,
one satellite was visible towards the west, very small, at a distance
of 2´ from Jupiter (Fig. 49).

Feb. 16: 6 h.—Their places were arranged as follows (Fig. 50); that is,
the satellite on the east was 7´ from Jupiter, Jupiter 5´ from the next
satellite on the west, and this 3´ from the remaining satellite still
further to the west. They were all of the same magnitude nearly, rather
bright, and in the same straight line, corresponding accurately to the
direction of the Zodiac.

Feb. 17: 1 h.—Two satellites were in view, one on the east, distant 3´
from Jupiter; the other on the west, distant 10´ (Fig. 51). The latter
was somewhat less than the satellite on the east; but at the sixth
hour the eastern satellite was nearer to Jupiter, being at a distance
of 0´ 50´´, and the western satellite was further off, namely 12´. At
both observations they were in the same straight line with Jupiter, and
were both rather small, especially the eastern satellite in the second
observation.

Feb. 18: 1 h.—Three satellites were in view, of which two were on
the west and one on the east; the distance of the eastern satellite
from Jupiter was 3´, and of the nearest satellite on the west 2´; the
remaining satellite, still further to the west, was 8´ from the middle
satellite (Fig. 52). They were all in the same straight line exactly,
and of about the same magnitude. But at the second hour the satellites
nearest to the planet were at equal distances from Jupiter, for the
western satellite was now also 3´ from the planet. But at the sixth
hour the fourth satellite was visible between the satellite on the east
and Jupiter, in the following configuration (Fig. 53). The satellite
furthest to the east was at a distance of 3´ from the next in order;
this one was at a distance of 1´ 50´´ from Jupiter; Jupiter was at a
distance of 3´ from the next satellite on the west, and this 7´ from
the satellite still further to the west. These were nearly equal in
magnitude, only the satellite on the east nearest to Jupiter was a
little smaller than the rest, and they were all in the same straight
line parallel to the ecliptic.

Feb. 19: 0 h. 40 m.—Two satellites only were in view, west of Jupiter,
rather large, and arranged exactly in the same straight line with
Jupiter, in the direction of the ecliptic (Fig. 54). The nearer
satellite was at a distance of 7´ from Jupiter and of 6´ from the
satellite further to the west.

Feb. 20.—The sky was cloudy.

Feb. 21: 1 h. 30 m.—Three satellites, rather small, were in view,
placed thus (Fig. 55). The satellite to the east was 2´ from Jupiter;
Jupiter was 3´ from the next, which was on the west; and this one was
7´ from the satellite further to the west. They were exactly in the
same straight line parallel to the ecliptic.

Feb. 25: 1 h. 30 m. (for on the three previous nights the sky was
overcast).—Three satellites appeared, two on the east, which were at a
distance of 4´ apart, the same as the distance of the nearer satellite
from Jupiter; on the west there was one satellite at a distance of
2´ from Jupiter. They were exactly in the same straight line in the
direction of the ecliptic (Fig. 56).

Feb. 26: 0 h. 30 m.—A pair of satellites only were present, one on
the east, distant 10´ from Jupiter; the other was on the west, at a
distance of 6´ (Fig. 57). The eastern satellite was slightly smaller
than the western. At the fifth hour three satellites were visible; for,
besides the two already noticed, a third satellite was in view, on the
west, near Jupiter, very small, which previously had been hidden behind
Jupiter, and it was at a distance of 1´ from the planet (Fig. 58).

But the satellite on the east was seen to be further off than before,
being at a distance of 11´ from Jupiter. On this night, for the first
time, I determined to observe the motion of Jupiter and the adjacent
planets (his satellites) along the zodiac, by reference to some fixed
star; for there was a fixed star in view, eastwards of Jupiter, at a
distance of 11´ from the satellite on the east, and a little to the
south, in the following manner (Fig. 59).

Feb. 27: 1 h. 4 m.—The satellites appeared in the following
configuration. The satellite furthest to the east was at a distance
of 10´ from Jupiter; the next in order was near Jupiter, being at a
distance of 0´ 30´´ from the planet. The next satellite was on the
western side, at a distance of 2´ 30´´ from Jupiter; and the satellite
further to the west was at a distance of 1´ from this. The two
satellites near to Jupiter appeared small, especially the satellite
on the east; but the satellites furthest off were very bright,
particularly that on the west, and they made a straight line in the
direction of the ecliptic exactly. The motion of the planets towards
the east was plainly seen by reference to the aforesaid fixed star, for
Jupiter and his attendant satellites were nearer to it, as may be seen
in the accompanying figure (Fig. 60). At the fifth hour the satellite
on the east, near to Jupiter, was 1´ from the planet.

Feb. 28: 1 h.—Only two satellites were visible, one on the east, at a
distance of 9´ from Jupiter, and another on the west, at a distance of
2´; they were both rather bright, and in the same straight line with
Jupiter, and a straight line drawn from the fixed star perpendicular
to this straight line fell upon the satellite on the east, as in the
figure (Fig. 61). At the fifth hour a third satellite was seen at a
distance of 2´ from Jupiter, on the east, in the position shown in the
figure (Fig. 62).

March 1: 0 h. 40 m.—Four satellites, all on the east of the planet,
were seen; the satellite nearest to Jupiter was 2´ from the planet;
the next 1´ from this; the third was 0´ 20´´ from the second, and was
brighter than the others; and the satellite still further to the east
was at a distance of 4´ from it, and was smaller than the others (Fig.
63). They made a straight line very nearly, only the satellite third
from Jupiter was slightly above the line. The fixed star formed with
Jupiter and the most easterly satellite an equilateral triangle, as in
the figure.

March 2: 0 h. 40 m.—Three satellites were in attendance, two on the
east and one on the west, in the configuration shown in the diagram
(Fig. 64). The satellite furthest to the east was 7´ from Jupiter; from
this satellite the next was distant 0´ 30´´, and the satellite on the
west was separated from Jupiter by an interval of 2´. The satellites
furthest off were brighter and larger than the remaining satellite,
which appeared very small. The satellite furthest to the east seemed to
be raised a little towards the north, out of the straight line drawn
through the other satellites and Jupiter.

The fixed star already noticed was at a distance of 8´ from the western
satellite, that is, from the perpendicular drawn from that satellite to
the straight line drawn through all the system, as shown in the figure
given.

These determinations of the motion of Jupiter and the adjacent planets
(his satellites) by reference to a fixed star, I have thought well
to present to the notice of astronomers, in order that any one may
be able to understand from them that the movements of these planets
(Jupiter’s satellites) both in longitude and in latitude agree exactly
with the motions [of Jupiter] which are extracted from tables.

These are my observations upon the four Medicean planets, recently
discovered for the first time by me; and although it is not yet
permitted me to deduce by calculation from these observations the
orbits of these bodies, yet I may be allowed to make some statements,
based upon them, well worthy of attention.

[Sidenote: Deductions from the previous observations concerning the
orbits and periods of Jupiter’s satellites.]

And, in the first place, since they are sometimes behind, sometimes
before Jupiter, at like distances, and withdraw from this planet
towards the east and towards the west only within very narrow limits of
divergence, and since they accompany this planet alike when its motion
is retrograde and direct, it can be a matter of doubt to no one that
they perform their revolutions about this planet, while at the same
time they all accomplish together orbits of twelve years’ length about
the centre of the world. Moreover, they revolve in unequal circles,
which is evidently the conclusion to be drawn from the fact that I
have never been permitted to see two satellites in conjunction when
their distance from Jupiter was great, whereas near Jupiter two, three,
and sometimes all (four), have been found closely packed together.
Moreover, it may be detected that the revolutions of the satellites
which describe the smallest circles round Jupiter are the most rapid,
for the satellites nearest to Jupiter are often to be seen in the east,
when the day before they have appeared in the west, and contrariwise.
Also the satellite moving in the greatest orbit seems to me, after
carefully weighing the occasions of its returning to positions
previously noticed, to have a periodic time of half a month.[17]
Besides, we have a notable and splendid argument to remove the scruples
of those who can tolerate the revolution of the planets round the Sun
in the Copernican system, yet are so disturbed by the motion of one
Moon about the Earth, while both accomplish an orbit of a year’s length
about the Sun, that they consider that this theory of the constitution
of the universe must be upset as impossible; for now we have not one
planet only revolving about another, while both traverse a vast orbit
about the Sun, but our sense of sight presents to us four satellites
circling about Jupiter, like the Moon about the Earth, while the whole
system travels over a mighty orbit about the Sun in the space of twelve
years.

    [17] In the edition of Galileo’s works published at Florence,
    1854, there are given the tables of the hourly movements of the
    satellites of Jupiter, from which Galileo determined their periods
    of revolution. In the beginning of his treatise on floating bodies,
    _Discorso intorno i Galleggianti_, 1611-12, Galileo gives the times
    of rotation as approximately, (i.) 1 d. 18-1/2 h.; (ii.) 3 d.
    13-1/3 h.; (iii.) 7 d. 4 h.; (iv.) 16 d. 18 h.; he also published
    configurations of the satellites calculated for March, April,
    and a part of May 1613. The periodic times of the satellites, as
    corrected by later observers, are, (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.

[Sidenote: Explanation of the variations in brightness of Jupiter’s
satellites.]

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._

    —————————+———————————+———————————————+———————————————
      FIG.   |  DATE.    |    EAST.      |    WEST.
    —————————+———————————+———————————————+———————————————
           1 | Jan.    7 |
             |           |   •      •    ◯       •
    —————————+———————————+———————————————————————————————
           2 |         8 |
             |           |               ◯  •   •   •
    —————————+———————————+———————————————————————————————
           3 |        10 |
             |           |       •    •  ◯
    —————————+———————————+———————————————————————————————
           4 |        11 |
             |           |      •   •    ◯
    —————————+———————————+———————————————————————————————
           5 |        12 |
             |           |           •  •◯    •
    —————————+———————————+—————————-—————————————————————
           6 |        13 |
             |           |          •    ◯ •  ⠁  •
    —————————+———————————+———————————————————————————————
           7 |        15 |                        •
             |           |               ◯   •  •     •
    —————————+———————————+———————————————————————————————
           8 |        15 |
             |           |               ◯     •  •    •
    —————————+———————————+———————————————————————————————
           9 |        16 |
             |           |             • ◯ •         •
    —————————+———————————+———————————————————————————————
          10 |        17 |
             |           |           •   ◯             •
    —————————+———————————+———————————————————————————————
          11 | Jan.   17 |           •              •
             |           |             • ◯
    —————————+———————————+———————————————————————————————
          12 |        18 |
             |           |      •        ◯           •
    —————————+———————————+———————————————————————————————
          13 |        19 |
             |           |        •      ◯      •     •
    —————————+———————————+———————————————————————————————
          14 |        19 |
             |           |        •  •   ◯    • •
    —————————+———————————+———————————————————————————————
          15 |        20 |
             |           |            •  ◯   • •
    —————————+———————————+———————————————————————————————
          16 |        20 |
             |           |           •   ◯  • •
    —————————+———————————+———————————————————————————————
          17 |        20 |             • ◯  •  •
             |           |                    •
    —————————+———————————+———————————————————————————————
          18 |        21 |
             |           |           • • ◯      •
    —————————+———————————+———————————————————————————————
          19 |        22 |          •    ◯•       •
             |           |                  •
    —————————+———————————+———————————————————————————————
          20 |        22 |
             |           |           •   ◯  •  • •
    —————————+———————————+———————————————————————————————
          21 |        23 |
             |           |      •    •   ◯   •
    —————————+———————————+———————————————————————————————
          22 |        23 |
             |           |     •         ◯
    —————————+———————————+———————————————————————————————
          23 |        24 |    •        • ◯
             |           |           •
    —————————+———————————+———————————————————————————————
          24 |        25 |
             |           |    •     •    ◯
    —————————+———————————+———————————————————————————————
          25 |        26 |
             |           |    •    •     ◯    •
    —————————+———————————+———————————————————————————————
          26 |        26 |             •
             |           |    •     •    ◯      •
    —————————+———————————+———————————————————————————————
          27 |        27 |
             |           |       •       ◯
    —————————+———————————+———————————————————————————————
          28 |        30 |                    •
             |           |            •  ◯      •
    —————————+———————————+———————————————————————————————
          29 |        31 |           •
             |           |         •     ◯           •
    —————————+———————————+———————————————————————————————
          30 | Jan.   31 |        •
             |           |       •       ◯        •
    —————————+———————————+———————————————————————————————
          31 | Feb.    1 |
             |           |     •       • ◯         •
    —————————+———————————+———————————————————————————————
          32 |         2 |
             |           |      •        ◯   •       •
    —————————+———————————+———————————————————————————————
          33 |         2 |
             |           |      •    •   ◯     •       •
    —————————+———————————+———————————————————————————————
          34 |         3 |
             |           |           •   ◯   •         •
    —————————+———————————+———————————————————————————————
          35 |         4 |
             |           |         •   • ◯     •     •
    —————————+———————————+———————————————————————————————
          36 |         4 |
             |           |          • •  ◯      •  •
    —————————+———————————+———————————————————————————————
          37 |         6 |
             |           |         •     ◯       •
    —————————+———————————+———————————————————————————————
          38 |         7 |
             |           |          • •  ◯
    —————————+———————————+———————————————————————————————
          39 |         8 |
             |           |     • •     • ◯
    —————————+———————————+———————————————————————————————
          40 |         9 |
             |           |       •   •   ◯     •
    —————————+———————————+———————————————————————————————
          41 |        10 |
             |           |       •     • ◯
    —————————+———————————+———————————————————————————————
          42 |        11 |
             |           |     •     •   ◯     •
    —————————+———————————+———————————————————————————————
          43 |        11 |             •
             |           |   •     •     ◯       •
    —————————+———————————+———————————————————————————————
          44 |        11 |
             |           |    •  •   •   ◯     •
    —————————+———————————+———————————————————————————————
          45 |        12 |
             |           |      •      • ◯ •    •
    —————————+———————————+———————————————————————————————
          46 |        13 |
             |           |       •     • ◯      • •
    —————————+———————————+———————————————————————————————
          47 |        15 |
             |           |         • • • ◯
    —————————+———————————+———————————————————————————————
          48 |        15 |
             |           |       •     • ◯
    —————————+———————————+———————————————————————————————
          49 | Feb.   15 |
             |           |      •      • ◯   •
    —————————+———————————+———————————————————————————————
          50 |        16 |
             |           |   •           ◯         •   •
    —————————+———————————+———————————————————————————————
          51 |        17 |
             |           |           •   ◯             •
    —————————+———————————+———————————————————————————————
          52 |        18 |
             |           |           •   ◯  •        •
    —————————+———————————+———————————————————————————————
          53 |        18 |
             |           |        •    • ◯   •        •
    —————————+———————————+———————————————————————————————
          54 |        19 |
             |           |               ◯         •    •
    —————————+———————————+———————————————————————————————
          55 |        21 |
             |           |           •   ◯   •        •
    —————————+———————————+———————————————————————————————
          56 |        25 |
             |           |   •      •    ◯    •
    —————————+———————————+———————————————————————————————
          57 |        26 |
             |           |    •          ◯       •
    —————————+———————————+———————————————————————————————
          58 |        26 |
             |           |    •          ◯ •     •
    —————————+———————————+———————————————————————————————
          59 |        26 |    •          ◯ •     •
             |           | ⨀ Star.
    —————————+———————————+———————————————————————————————
          60 |        27 |      •      • ◯ • •
             |           | Star ⨀
    —————————+———————————+———————————————————————————————
          61 |        28 |       •       ◯  •
             |           |  Star ⨀
    —————————+———————————+———————————————————————————————
          62 |        28 |
             |           |         •   • ◯ •
    —————————+———————————+———————————————————————————————
          63 | Mar.    1 |          •
             |           |        •  • • ◯
             |           |        Star ⨀
    —————————+———————————+———————————————————————————————
          64 |         2 |        •
             |           |          •    ◯ •
             |           |                        Star ⨀
    —————————+———————————+———————————————————————————————



    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.

[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).

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.

    “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.

    [30] 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.

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.





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