_Spots on the Sun—Essay on Floating Bodies—Scheiner—Change in
Saturn._
GALILEO did not indulge the curiosity of his Roman friends by exhibiting
only the wonders already mentioned, which now began to lose the gloss of
novelty, but disclosed a new discovery, which appeared still more
extraordinary, and, to the opposite faction, more hateful than anything
of which he had yet spoken. This was the discovery, which he first made
in the month of March, 1611, of dark spots on the body of the sun. A
curious fact, and one which well serves to illustrate Galileo's
superiority in seeing things simply as they are, is, that these spots
had been observed and recorded centuries before he existed, but, for
want of careful observation, their true nature had been constantly
misapprehended. One of the most celebrated occasions was in the year 807
of our era, in which a dark spot is mentioned as visible on the face of
the sun during seven or eight days. It was then supposed to be
Mercury.[67] Kepler, whose astronomical knowledge would not suffer him
to overlook that it was impossible that Mercury could remain so long in
conjunction with the sun, preferred to solve the difficulty by supposing
that, in Aimoin's original account, the expression was not _octo dies_
(eight days), but _octoties_—a barbarous word, which he supposed to
have been written for _octies_ (eight times); and that the other
accounts (in which the number of days mentioned is different) copying
loosely from the first, had both mistaken the word, and misquoted the
time which they thought they found mentioned there. It is impossible to
look on this explanation as satisfactory, but Kepler, who at that time
did not dream of spots on the sun, was perfectly contented with it. In
1609, he himself observed upon the sun a black spot, which he in like
manner mistook for Mercury, and unluckily the day, being cloudy, did
not allow him to contemplate it sufficiently long to discover his
error, which the slowness of its apparent motion would soon have pointed
out.[68] He hastened to publish his supposed observation, but no sooner
was Galileo's discovery of the solar spots announced, than he, with that
candour which as much as his flighty disposition certainly characterized
him at all times, retracted his former opinion, and owned his belief
that he had been mistaken. In fact it is known from the more accurate
theory which we now possess of Mercury's motions, that it did not pass
over the sun's face at the time when Kepler thought he perceived it
there.
Galileo's observations were in their consequences to him particularly
unfortunate, as in the course of the controversy in which they engaged
him, he first became personally embroiled with the powerful party, whose
prevailing influence was one of the chief causes of his subsequent
misfortunes. Before we enter upon that discussion, it will be proper to
mention another famous treatise which Galileo produced soon after his
return from Rome to Florence, in 1612. This is, his Discourse on
Floating Bodies, which restored Archimedes' theory of hydrostatics, and
has, of course, met with the opposition which few of Galileo's works
failed to encounter. In the commencement, he thought it necessary to
apologize for writing on a subject so different from that which chiefly
occupied the public attention, and declared that he had been too closely
occupied in calculating the periods of the revolutions of Jupiter's
satellites to permit him to publish anything earlier. These periods he
had succeeded in determining during the preceding year, whilst at Rome,
and he now announced them to complete their circuits, the first in about
1 day, 18½ hours; the second in 3 days, 13 hours, 20 minutes; the third
in 7 days, 4 hours; and the outermost in 16 days, 18 hours. All these
numbers he gave merely as approximately true, and promised to continue
his observations, for the purpose of correcting the results. He then
adds an announcement of his recent discovery of the solar spots, "which,
as they change their situation, offer a strong argument, either that the
sun revolves on itself, or that, perhaps, other stars, like Venus and
Mercury, revolve about it, invisible at all other times, on account of
the small distance to which they are removed from him." To this he
afterwards subjoined, that, by continued observation, he had satisfied
himself that these solar spots were in actual contact with the surface
of the sun, where they are continually appearing and disappearing; that
their figures were very irregular, some being very dark, and others not
so black; that one would often divide into three or four, and, at other
times, two, three, or more would unite into one; besides which, that
they had all a common and regular motion, with which they revolved round
with the sun, which turned upon its axis in about the time of a lunar
month.
Having by these prefatory observations assuaged the public thirst for
astronomical novelties, he ventures to introduce the principal subject
of the treatise above mentioned. The question of floating bridges had
been discussed at one of the scientific parties, assembled at the house
of Galileo's friend Salviati, and the general opinion of the company
appearing to be that the floating or sinking of a body depended
principally upon its shape, Galileo undertook to convince them of their
error. If he had not preferred more direct arguments, he might merely
have told them that in this instance they were opposed to their
favourite Aristotle, whose words are very unequivocal on the point in
dispute. "Form is not the cause why a body moves downwards rather than
upwards, but it does affect the swiftness with which it moves;"[69]
which is exactly the distinction which those who called themselves
Aristotelians were unable to perceive, and to which the opinions of
Aristotle himself were not always true. Galileo states the discussion to
have immediately arisen from the assertion of some one in the company,
that condensation is the effect of cold, and ice was mentioned as an
instance. On this, Galileo observed, that ice is rather water rarefied
than condensed, the proof of which is, that ice always floats upon
water.[70] It was replied, that the reason of this phenomenon was, not
the superior lightness of the ice, but its incapacity, owing to its flat
shape, to penetrate and overcome the resistance of the water. Galileo
denied this, and asserted that ice of any shape would float upon water,
and that, if a flat piece of ice were forcibly taken to the bottom, it
would of itself rise again to the surface. Upon this assertion it
appears that the conversation became so clamorous, that Galileo thought
it pertinent to commence his Essay with the following observation on the
advantage of delivering scientific opinions in writing, "because in
conversational arguments, either one or other party, or perhaps both,
are apt to get overwarm, and to speak overloud, and either do not suffer
each other to be heard, or else, transported with the obstinacy of not
yielding, wander far away from the original proposition, and confound
both themselves and their auditors with the novelty and variety of their
assertions." After this gentle rebuke he proceeds with his argument, in
which he takes occasion to state the famous hydrostatical paradox, of
which the earliest notice is to be found in Stevin's works, a
contemporary Flemish engineer, and refers it to a principle on which we
shall enlarge in another chapter. He then explains the true theory of
buoyancy, and refutes the false reasoning on which the contrary opinions
were founded, with a variety of experiments.
The whole value and interest of experimental processes generally depends
on a variety of minute circumstances, the detail of which would be
particularly unsuited to a sketch like the present one. For those who
are desirous of becoming more familiar with Galileo's mode of conducting
an argument, it is fortunate that such a series of experiments exists as
that contained in this essay; experiments which, from their simplicity,
admit of being for the most part concisely enumerated, and at the same
time possess so much intrinsic beauty and characteristic power of
forcing conviction. They also present an admirable specimen of the
talent for which Galileo was so deservedly famous, of inventing
ingenious arguments in favour of his adversaries' absurd opinions before
he condescended to crush them, shewing that nothing but his love of
truth stood in the way of his being a more subtle sophist than any
amongst them. In addition to these reasons for giving these experiments
somewhat in detail, is the fact that all explanation of one of the
principal phenomena to which they allude is omitted in many more modern
treatises on Hydrostatics; and in some it is referred precisely to the
false doctrines here confuted.
The marrow of the dispute is included in Galileo's assertion, that "The
diversity of figure given to any solid cannot be in any way the cause of
its absolutely sinking or floating; so that if a solid, when formed for
example into a spherical figure, sinks or floats in the water, the same
body will sink or float in the same water, when put into any other form.
The breadth of the figure may indeed retard its velocity, as well of
ascent as descent, and more and more according as the said figure is
reduced to a greater breadth and thinness; but that it may be reduced to
such a form as absolutely to put an end to its motion in the same fluid,
I hold to be impossible. In this I have met with great contradictors
who, producing some experiments, and in particular a thin board of
ebony, and a ball of the same wood, and shewing that the ball in water
sinks to the bottom[71], and that the board if put lightly on the
surface floats, have held and confirmed themselves in their opinion with
the authority of Aristotle, that the cause of that rest is the breadth
of the figure, unable by its small weight to pierce and penetrate the
resistance of the water's thickness, which is readily overcome by the
other spherical figure."—For the purpose of these experiments, Galileo
recommends a substance such as wax, which may be easily moulded into any
shape, and with which, by the addition of a few filings of lead, a
substance may be readily made of any required specific gravity. He then
declares that if a ball of wax of the size of an orange, or bigger, be
made in this manner heavy enough to sink to the bottom, but so lightly
that if we take from it only one grain of lead it returns to the top;
and if the same wax be afterwards moulded into a broad and thin cake, or
into any other figure, regular or irregular, the addition of the same
grain of lead will always make it sink, and it will again rise when we
remove the lead from it.—"But methinks I hear some of the adversaries
raise a doubt upon my produced experiment: and, first, they offer to my
consideration that the figure, as a figure simply, and disjunct from the
matter, works no effect, but requires to be conjoined with the matter;
and, moreover, not with every matter, but with those only wherewith it
may be able to execute the desired operation. Just as we see by
experience that an acute and sharp angle is more apt to cut than an
obtuse; yet always provided that both one and the other are joined with
a matter fit to cut, as for instance, steel. Therefore a knife with a
fine and sharp edge cuts bread or wood with much ease, which it will not
do if the edge be blunt and thick; but if, instead of steel, any one
will take wax and mould it into a knife, undoubtedly he will never learn
the effects of sharp and blunt edges, because neither of them will cut;
the wax being unable, by reason of its flexibility, to overcome the
hardness of the wood and bread. And therefore, applying the like
discourse to our argument, they say that the difference of figure will
shew different effects with regard to floating and sinking, but not
conjoined with any kind of matter, but only with those matters which by
their weight are able to overcome the viscosity of the water (like the
ebony which they have selected); and he that will select cork or other
light wood to form solids of different figures, would in vain seek to
find out what operation figure has in sinking or floating, because all
would swim, and that not through any property of this or that figure,
but through the debility of the matter.
"When I begin to examine one by one all the particulars here produced, I
allow not only that figures, simply as such, do not operate in natural
things, but also that they are never separated from the corporeal
substance, nor have I ever alleged them to be stript of sensible matter:
and also I freely admit, that in our endeavours to examine the diversity
of accidents which depend upon the variety of figures, it is necessary
to apply them to matters which obstruct not the various operations of
those various figures. I admit and grant that I should do very ill if I
were to try the influence of a sharp edge with a knife of wax, applying
it to cut an oak, because no sharpness in wax is able to cut that very
hard wood. But yet, such an experiment of this knife would not be beside
the purpose to cut curded milk, or other very yielding matter; nay, in
such matters, the wax is more convenient than steel for finding the
difference depending on the acuteness of the angles, because milk is cut
indifferently with a razor, or a blunt knife. We must therefore have
regard not only to the hardness, solidity, or weight of the bodies
which, under different figures, are to divide some matters asunder; but
also, on the other hand, to the resistance of the matter to be
penetrated. And, since I have chosen a matter which does penetrate the
resistance of the water, and in all figures descends to the bottom, my
antagonists can charge me with no defect; nor (to revert to their
illustration) have I attempted to test the efficacy of acuteness by
cutting with matters unable to cut. I subjoin withal, that all caution,
distinction, and election of matter would be superfluous and
unnecessary, if the body to be cut should not at all resist the cutting:
if the knife were to be used in cutting a mist, or smoke, one of paper
would serve the purpose as well as one of Damascus steel; and I assert
that this is the case with water, and that there is not any solid of
such lightness or of such a figure, that being put on the water it will
not divide and penetrate its thickness; and if you will examine more
carefully your thin boards of wood, you will see that they have part of
their thickness under water; and, moreover, you will see that the
shavings of ebony, stone, or metal, when they float, have not only thus
broken the continuity of the water, but are with all their thickness
under the surface of it; and that more and more, according as the
floating substance is heavier, so that a thin floating plate of lead
will be lower than the surface of the surrounding water by at least
twelve times the thickness of the plate, and gold will dive below the
level of the water almost twenty times the thickness of the plate, as I
shall shew presently."
In order to illustrate more clearly the non-resistance of water to
penetration, Galileo then directs a cone to be made of wood or wax, and
asserts that when it floats, either with its base or point in the water,
the solid content of the part immersed will be the same, although the
point is, by its shape, better adapted to overcome the resistance of the
water to division, if that were the cause of the buoyancy. Or the
experiment may be varied by tempering the wax with filings of lead, till
it sinks in the water, when it will be found that in any figure the same
cork must be added to it to raise it to the surface.—"This silences not
my antagonists; but they say that all the discourse hitherto made by me
imports little to them, and that it serves their turn, that they have
demonstrated in one instance, and in such manner and figure as pleases
them best, namely, in a board and a ball of ebony, that one, when put
into the water, sinks to the bottom, and that the other stays to swim at
the top; and the matter being the same, and the two bodies differing in
nothing but in figure, they affirm that with all perspicuity they have
demonstrated and sensibly manifested what they undertook. Nevertheless I
believe, and think I can prove that this very experiment proves nothing
against my theory. And first it is false that the ball sinks, and the
board not; for the board will sink too, if you do to both the figures as
the words of our question require; that is, if you put them both _in_
the water; for to be in the water implies to be placed in the water, and
by Aristotle's own definition of place, to be placed imports to be
environed by the surface of the ambient body; but when my antagonists
shew the floating board of ebony, they put it not into the water, but
upon the water; where, being detained by a certain impediment (of which
more anon) it is surrounded, partly with water, partly with air, which
is contrary to our agreement, for that was that the bodies should be in
the water, and not part in the water, part in the air. I will not omit
another reason, founded also upon experience, and, if I deceive not
myself, conclusive against the notion that figure, and the resistance of
the water to penetration have anything to do with the buoyancy of
bodies. Choose a piece of wood or other matter, as for instance
walnut-wood, of which a ball rises from the bottom of the water to the
surface more slowly than a ball of ebony of the same size sinks, so that
clearly the ball of ebony divides the water more readily in sinking than
does the walnut in rising. Then take a board of walnut-tree equal to and
like the floating ebony one of my antagonists; and if it be true that
this latter floats by reason of the figure being unable to penetrate the
water, the other of walnut-tree, without all question, if thrust to the
bottom ought to stay there, as having the same impeding figure, and
being less apt to overcome the said resistance of the water. But if we
find by experience that not only the thin board, but every other figure
of the same walnut-tree will return to float, as unquestionably we
shall, then I must desire my opponents to forbear to attribute the
floating of the ebony to the figure of the board, since the resistance
of the water is the same in rising as in sinking, and the force of
ascension of the walnut-tree is less than the ebony's force for going to
the bottom.
"Now, let us return to the thin plate of gold or silver, or the thin
board of ebony, and let us lay it lightly upon the water, so that it may
stay there without sinking, and carefully observe the effect. It will
appear clearly that the plates are a considerable matter lower than the
surface of the water which rises up, and makes a kind of rampart round
them on every side, in the manner shewn in the annexed figure, in which
BDLF represents the surface of the water, and AEIO the surface of the
plate. But if it have already penetrated and overcome the continuity of
the water, and is of its own nature heavier than the water, why does it
not continue to sink, but stop and suspend itself in that little dimple
that its weight has made in the water? My answer is, because in sinking
till its surface is below the water which rises up in a bank round it,
it draws after and carries along with it the air above it, so that that
which in this case descends and is placed in the water, is not only the
board of ebony or plate of iron, but a compound of ebony and air, from
which composition results a solid no longer specifically heavier than
the water, as was the ebony or gold alone. But, Gentlemen, we want the
same matter; you are to alter nothing but the shape, and therefore have
the goodness to remove this air, which may be done simply by washing the
upper surface of the board, for the water having once got between the
board and air will run together, and the ebony will go to the bottom;
and if it does not, you have won the day. But methinks I hear some of my
antagonists cunningly opposing this, and telling me that they will not
on any account allow their board to be wetted, because the weight of the
water so added, by making it heavier than it was before, draws it to the
bottom, and that the addition of new weight is contrary to our
agreement, which was that the matter should be the same."
[Illustration]
"To this I answer first, that nobody can suppose bodies to be put into
the water without their being wet, nor do I wish to do more to the
board than you may do to the ball. Moreover, it is not true that the
board sinks on account of the weight of the water added in the washing;
for I will put ten or twenty drops on the floating board, and so long as
they stand separate it shall not sink; but if the board be taken out,
and all that water wiped off, and the whole surface bathed with one
single drop, and put it again upon the water, there is no question but
it will sink, the other water running to cover it, being no longer
hindered by the air. In the next place it is altogether false that water
can in any way increase the weight of bodies immersed in it, for water
has no weight in water, since it does not sink. Now, just as he who
should say that brass by its own nature sinks, but that when formed into
the shape of a kettle, it acquires from that figure a virtue of lying in
the water without sinking, would say what is false, because that is not
purely brass which then is put into the water, but a compound of brass
and air; so is it neither more nor less false, that a thin plate of
brass or ebony swims by virtue of its dilated and broad figure. Also I
cannot omit to tell my opponents, that this conceit of refusing to bathe
the surface of the board, might beget an opinion in a third person of a
poverty of arguments on their side, especially as the conversation began
about flakes of ice, in which it would be simple to require that the
surfaces should be kept dry; not to mention that such pieces of ice,
whether wet or dry, always float, and as my antagonists say, because of
their shape.
"Some may wonder that I affirm this power to be in the air of keeping
the plate of brass or silver above water, as if in a certain sense I
would attribute to the air a kind of magnetic virtue for sustaining
heavy bodies with which it is in contact. To satisfy all these doubts, I
have contrived the following experiment to demonstrate how truly the air
does support these solids; for I have found, when one of these bodies
which floats when placed lightly on the water, is thoroughly bathed and
sunk to the bottom, that by carrying down to it a little air without
otherwise touching it in the least, I am able to raise and carry it back
to the top, where it floats as before. To this effect I take a ball of
wax, and with a little lead make it just heavy enough to sink very
slowly to the bottom, taking care that its surface be quite smooth and
even. This, if put gently into the water, submerges almost entirely,
there remaining visible only a little of the very top, which, so long as
it is joined to the air, keeps the ball afloat; but if we take away the
contact of the air by wetting this top, the ball sinks to the bottom,
and remains there. Now to make it return to the surface by virtue of the
air which before sustained it, thrust into the water a glass, with the
mouth downwards, which will carry with it the air it contains; and move
this down towards the ball, until you see by the transparency of the
glass that the air has reached the top of it; then gently draw the glass
upwards, and you will see the ball rise, and afterwards stay on the top
of the water, if you carefully part the glass and water without too much
disturbing it.[72] There is therefore a certain affinity between the air
and other bodies, which holds them united, so that they separate not
without a kind of violence, just as between water and other bodies; for
in drawing them wholly out of the water, we see the water follow them,
and rise sensibly above the level before it quits them." Having
established this principle by this exceedingly ingenious and convincing
experiment, Galileo proceeds to shew from it what must be the dimensions
of a plate of any substance which will float as the wax does, assuming
in each case that we know the greatest height at which the rampart of
water will stand round it. In like manner he shows that a pyramidal or
conical figure may be made of any substance, such that by help of the
air, it shall rest upon the water without wetting more than its base;
and that we may so form a cone of any substance that it shall float if
placed gently on the surface, with its point downwards, whereas no care
or pains will enable it to float with its base downwards, owing to the
different proportions of air which in the two positions remain connected
with it. With this parting blow at his antagonist's theory we close our
extracts from this admirable essay.
The first elements of the theory of running waters were reserved for
Castelli, an intimate friend and pupil of Galileo. On the present
occasion, Castelli appeared as the ostensible author of a defence
against the attacks made by Vincenzio di Grazia and by Lodovico delle
Columbe (the author of the crystalline composition of the moon) on the
obnoxious theory. After destroying all the objections which they
produced, the writer tauntingly bids them remember, that he was merely
Galileo's pupil, and consider how much more effectually Galileo himself
would have confuted them, had he thought it worth while. It was not
known till several years after his death, that this Essay was in fact
written by Galileo himself.[73]
These compositions merely occupied the leisure time which he could
withhold from the controversy on the solar spots to which we have
already alluded. A German Jesuit named Christopher Scheiner, who was
professor of mathematics at Ingolstadt, in imitation of Galileo had
commenced a series of observations on them, but adopted the theory
which, as we have seen, Galileo had examined and rejected, that these
spots are planets circulating at some distance from the body of the sun.
The same opinion had been taken up by a French astronomer, who in honour
of the reigning family called them Borbonian stars. Scheiner promulgated
his notions in three letters, addressed to their common friend Welser,
under the quaint signature of "_Apelles latens post tabulam_." Galileo
replied to Scheiner's letters by three others, also addressed to Welser,
and although the dispute was carried on amid mutual professions of
respect and esteem, it laid the foundation of the total estrangement
which afterwards took place between the two authors. Galileo's part of
this controversy was published at Rome by the Lyncean Academy in 1613.
To the last of his letters, written in December, 1612, is annexed a
table of the expected positions of Jupiter's satellites during the
months of March and April of the following year, which, imperfect as it
necessarily was, cannot be looked upon without the greatest interest.
In the same letter it is mentioned that Saturn presented a novel
appearance, which, for an instant, almost induced Galileo to mistrust
the accuracy of his earlier observations. The lateral appendages of this
planet had disappeared, and the accompanying extract will show the
uneasiness which Galileo could not conceal at the sight of this
phenomenon, although it is admirable to see the contempt with which,
even in that trying moment, he expresses his consciousness that his
adversaries were unworthy of the triumph they appeared on the point of
celebrating.—"Looking on Saturn within these few days, I found it
solitary, without the assistance of its accustomed stars, and in short,
perfectly round and defined like Jupiter, and such it still remains. Now
what can be said of so strange a metamorphosis? are perhaps the two
smaller stars consumed, like the spots on the sun? have they suddenly
vanished and fled? or has Saturn devoured his own children? or was the
appearance indeed fraud and illusion, with which the glasses have for so
long a time mocked me, and so many others who have often observed with
me. Now perhaps the time is come to revive the withering hopes of those,
who, guided by more profound contemplations, have fathomed all the
fallacies of the new observations and recognised their impossibility! I
cannot resolve what to say in a chance so strange, so new, and so
unexpected; the shortness of the time, the unexampled occurrence, the
weakness of my intellect, and the terror of being mistaken, have greatly
confounded me." These first expressions of alarm are not to be wondered
at; however, he soon recovered courage, and ventured to foretel the
periods at which the lateral stars would again show themselves,
protesting at the same time, that he was in no respect to be understood
as classing this prediction among the results which depend on certain
principles and sound conclusions, but merely on some conjectures which
appeared to him probable. From one of the Dialogues on the System, we
learn that this conjecture was, that Saturn might revolve upon his axis,
but the period which he assumed is very different from the true one, as
might be expected from its being intended to account for a phenomenon of
which Galileo had not rightly apprehended the character.
He closed this letter with renewed professions of courtesy and
friendship towards Apelles, enjoining Welser not to communicate it
without adding his excuses, if he should be thought to dissent too
violently from his antagonist's ideas, declaring that his only object
was the discovery of truth, and that he had freely exposed his own
opinion, which he was still ready to change, so soon as his errors
should be made manifest to him; and that he would consider himself
under special obligation to any one who would be kind enough to discover
and correct them. These letters were written from the villa of his
friend Salviati at Selve near Florence, where he passed great part of
his time, particularly during his frequent indispositions, conceiving
that the air of Florence was prejudicial to him. Cesi was very anxious
for their appearance, since they were (in his own words) so hard a
morsel for the teeth of the Peripatetics, and he exhorted Galileo, in
the name of the society, "to continue to give them, and the nameless
Jesuit, something to gnaw."
FOOTNOTES:
[67] Aimoini Hist. Francorum. Parisiis. 1567.
[68] Mercurius in sole visus. 1609.
[69] De Cœlo. lib. 4.
[70] For a discussion of this singular phenomenon, _see_ Treatise on
Heat, p. 12; and it is worth while to remark in passing, what an
admirable instance it affords of Galileo's instantaneous abandonment of
a theory so soon as it became inconsistent with experiment.
[71] Ebony is one of the few woods heavier than water. _See_ Treatise on
Hydrostatics.
[72] In making this very beautiful experiment, it is best to keep the
glass a few seconds in the water, to give time for the surface of the
ball to dry. It will also succeed with a light needle, if carefully
conducted.
[73] Nelli. Saggio di Stor. Liter. Fiorent.