_Extracts from the Dialogues on the System._
AFTER narrating the treatment to which Galileo was subject on account of
his admirable Dialogues, it will not be irrelevant to endeavour, by a
few extracts, to convey some idea of the style in which they are
written. It has been mentioned, that he is considered to surpass all
other Italian writers (unless we except Machiavelli) in the purity and
beauty of his language, and indeed his principal followers, who avowedly
imitated his style, make a distinguished group among the classical
authors of modern Italy. He professed to have formed himself from the
study of Ariosto, whose poems he passionately admired, insomuch that he
could repeat the greater part of them, as well as those of Berni and
Petrarca, all which he was in the frequent habit of quoting in
conversation. The fashion and almost universal practice of that day was
to write on philosophical subjects in Latin; and although Galileo wrote
very passably in that language, yet he generally preferred the use of
Italian, for which he gave his reasons in the following characteristic
manner:—
"I wrote in Italian because I wished every one to be able to read what I
wrote; and for the same cause I have written my last treatise in the
same language: the reason which has induced me is, that I see young men
brought together indiscriminately to study to become physicians,
philosophers, &c., and whilst many apply to such professions who are
most unfit for them, others who would be competent remain occupied
either with domestic business, or with other employments alien to
literature; who, although furnished, as Ruzzante might say, with a
_decent set of brains_, yet, not being able to understand things written
in _gibberish_, take it into their heads, that in these crabbed folios
there must be some grand _hocus pocus_ of logic and philosophy much too
high up for them to think of jumping at. I want them to know, that as
Nature has given eyes to them just as well as to philosophers for the
purpose of seeing her works, she has also given them brains for
examining and understanding them."
The general structure of the dialogues has been already described;[93]
we shall therefore premise no more than the judgment pronounced on them
by a highly gifted writer, to supply the deficiencies of our necessarily
imperfect analysis.
"One forms a very imperfect idea of Galileo, from considering the
discoveries and inventions, numerous and splendid as they are, of which
he was the undisputed author. It is by following his reasonings, and by
pursuing the train of his thoughts, in his own elegant, though somewhat
diffuse exposition of them, that we become acquainted with the fertility
of his genius—with the sagacity, penetration, and comprehensiveness of
his mind. The service which he rendered to real knowledge is to be
estimated, not only from the truths which he discovered, but from the
errors which he detected—not merely from the sound principles which he
established, but from the pernicious idols which he overthrew. The
dialogues on the system are written with such singular felicity, that
one reads them at the present day, when the truths contained in them are
known and admitted, with all the delight of novelty, and feels one's
self carried back to the period when the telescope was first directed to
the heavens, and when the earth's motion, with all its train of
consequences, was proved for the first time."[94]
The first Dialogue is opened by an attack upon the arguments by which
Aristotle pretended to determine _à priori_ the necessary motions
belonging to different parts of the world, and on his favourite
principle that particular motions belong naturally to particular
substances. Salviati (representing Galileo) then objects to the
Aristotelian distinctions between the corruptible elements and
incorruptible skies, instancing among other things the solar spots and
newly appearing stars, as arguments that the other heavenly bodies may
probably be subjected to changes similar to those which are continually
occurring on the earth, and that it is the great distance alone which
prevents their being observed. After a long discussion on this point,
Sagredo exclaims, "I see into the heart of Simplicio, and perceive that
he is much moved by the force of these too conclusive arguments; but
methinks I hear him say—'Oh, to whom must we betake ourselves to settle
our disputes if Aristotle be removed from the chair? What other author
have we to follow in our schools, our studies, and academies? What
philosopher has written on all the parts of Natural Philosophy, and so
methodically as not to have overlooked a single conclusion? Must we then
desolate this fabric, by which so many travellers have been sheltered?
Must we destroy this asylum, this Prytaneum wherein so many students
have found a convenient resting-place, where without being exposed to
the injuries of the weather, one may acquire an intimate knowledge of
nature, merely by turning over a few leaves? Shall we level this
bulwark, behind which we are safe from every hostile attack?' I pity him
no less than I do one who at great expense of time and treasure, and
with the labour of hundreds, has built up a very noble palace; and then,
because of insecure foundations, sees it ready to fall—unable to bear
that those walls be stripped that are adorned with so many beautiful
pictures, or to suffer those columns to fall that uphold the stately
galleries, or to see ruined the gilded roofs, the chimney-pieces, the
friezes, and marble cornices erected at so much cost, he goes about it
with girders and props, with shores and buttresses, to hinder its
destruction."
Salviati proceeds to point out the many points of similarity between the
earth and moon, and among others which we have already mentioned, the
following remark deserves especial notice:—
"Just as from the mutual and universal tendency of the parts of the
earth to form a whole, it follows that they all meet together with equal
inclination, and that they may unite as closely as possible, assume the
spherical form; why ought we not to believe that the moon, the sun, and
other mundane bodies are also of a round figure, from no other reason
than from a common instinct and natural concourse of all their component
parts; of which if by accident any one should be violently separated
from its whole, is it not reasonable to believe that spontaneously, and
of its natural instinct, it would return? It may be added that if any
centre of the universe may be assigned, to which the whole terrene globe
if thence removed would seek to return, we shall find most probable that
the sun is placed in it, as by the sequel you shall understand."
Many who are but superficially acquainted with the History of Astronomy,
are apt to suppose that Newton's great merit was in his being the first
to suppose an attractive force existing in and between the different
bodies composing the solar system. This idea is very erroneous; Newton's
discovery consisted in conceiving and proving the identity of the force
with which a stone falls, and that by which the moon falls, towards the
earth (on an assumption that this force becomes weaker in a certain
proportion as the distance increases at which it operates), and in
generalizing this idea, in applying it to all the visible creation, and
tracing the principle of universal gravitation with the assistance of a
most refined and beautiful geometry into many of its most remote
consequences. But the general notion of an attractive force between the
sun, moon, and planets, was very commonly entertained before Newton was
born, and may be traced back to Kepler, who was probably the first
modern philosopher who suggested it. The following extraordinary
passages from his "Astronomy" will shew the nature of his conceptions on
this subject:—
"The true doctrine of gravity is founded on these axioms: every
corporeal substance, so far forth as it is corporeal, has a natural
fitness for resting in every place where it may be situated by itself
beyond the sphere of influence of its cognate body. Gravity is a mutual
affection between cognate bodies towards union or conjunction (similar
in kind to the magnetic virtue), so that the earth attracts a stone much
rather than the stone seeks the earth. Heavy bodies (if in the first
place we put the earth in the centre of the world) are not carried to
the centre of the world in its quality of centre of the world, but as to
the centre of a cognate round body, namely the earth. So that
wheresoever the earth may be placed or whithersoever it may be carried
by its animal faculty, heavy bodies will always be carried towards it.
If the earth were not round heavy bodies would not tend from every side
in a straight line towards the centre of the earth, but to different
points from different sides. If two stones were placed in any part of
the world near each other and beyond the sphere of influence of a third
cognate body, these stones, like two magnetic needles, would come
together in the intermediate point, each approaching the other by a
space proportional to the comparative mass of the other. If the moon
and earth were not retained in their orbits by their animal force or
some other equivalent, the earth would mount to the moon by a
fifty-fourth part of their distance, and the moon fall towards the earth
through the other fifty-three parts, and would there meet, assuming
however that the substance of both is of the same density. If the earth
should cease to attract its waters to itself, all the waters of the sea
would be raised, and would flow to the body of the moon."[95]
He also conjectured that the irregularities in the moon's motion were
caused by the joint action of the sun and earth, and recognized the
mutual action of the sun and planets, when he declared the mass and
density of the sun to be so great that the united attraction of the
other planets cannot remove it from its place. Among these bold and
brilliant ideas, his temperament led him to introduce others which show
how unsafe it was to follow his guidance, and which account for, if they
do not altogether justify, the sarcastic remark of Ross, that "Kepler's
opinion that the planets are moved round by the sunne, and that this is
done by sending forth a magnetic virtue, and that the sun-beames are
like the teethe of a wheele taking hold of the planets, are senslesse
crotchets fitter for a wheeler or a miller than a philosopher."[96]
Roberval took up Kepler's notions, especially in the tract which he
falsely attributed to Aristarchus, and it is much to be regretted that
Roberval should deserve credit for anything connected with that impudent
fraud. The principle of universal gravitation, though not the varying
proportion, is distinctly assumed in it, as the following passages will
sufficiently prove: "In every single particle of the earth, and the
terrestrial elements, is a certain property or accident which we suppose
common to the whole system of the world, by virtue of which all its
parts are forced together, and reciprocally attract each other; and this
property is found in a greater or less degree in the different
particles, according to their density. If the earth be considered by
itself, its centres of magnitude and virtue, or gravity, as we usually
call it, will coincide, to which all its parts tend in a straight line,
as well by their own exertion or gravity, as by the reciprocal
attraction of all the rest." In a subsequent chapter, Roberval repeats
these passages nearly in the same words, applying them to the whole
solar system, adding, that "the force of this attraction is not to be
considered as residing in the centre itself, as some ignorant people
think, but in the whole system whose parts are equally disposed round
the centre."[97] This very curious work was reprinted in the third
volume of the _Reflexiones Physico-Mathematicæ_ of Mersenne, from whom
Roberval pretended to have received the Arabic manuscript, and who is
thus irretrievably implicated in the forgery.[98] The last remark,
denying the attractive force to be due to any property of the central
point, seems aimed at Aristotle, who, in a no less curious passage,
maintaining exactly the opposite opinion, says, "Hence, we may better
understand what the ancients have related, that like things are wont to
have a tendency to each other. For this is not absolutely true; for if
the earth were to be removed to the place now occupied by the moon, no
part of the earth would then have a tendency towards that place, but
would still fall towards the point which the earth's centre now
occupies."[99] Mersenne considered the consequences of the attractive
force of each particle of matter so far as to remark, that if a body
were supposed to fall towards the centre of the earth, it would be
retarded by the attraction of the part through which it had already
fallen.[100] Galileo had not altogether neglected to speculate on such a
supposition, as is plain from the following extract. It is taken from a
letter to Carcaville, dated from Arcetri, in 1637. "I will say farther,
that I have not absolutely and clearly satisfied myself that a heavy
body would arrive sooner at the centre of the earth, if it began to fall
from the distance only of a single yard, than another which should start
from the distance of a thousand miles. I do not affirm this, but I offer
it as a paradox."[101]
It is very difficult to offer any satisfactory comment upon this
passage; it may be sufficient to observe that this paradoxical result
was afterwards deduced by Newton, as one of the consequences of the
general law with which all nature is pervaded, but with which there is
no reason to believe that Galileo had any acquaintance; indeed the idea
is fully negatived by other passages in this same letter. This is one of
the many instances from which we may learn to be cautious how we invest
detached passages of the earlier mathematicians with a meaning which in
many cases their authors did not contemplate. The progressive
development of these ideas in the hands of Wallis, Huyghens, Hook, Wren,
and Newton, would lead us too far from our principal subject. There is
another passage in the third dialogue connected with this subject, which
it may be as well to notice in this place. "The parts of the earth have
such a propensity to its centre, that when it changes its place,
although they may be very distant from the globe at the time of the
change, yet must they follow. An example similar to this is the
perpetual sequence of the Medicean stars, although always separated from
Jupiter. The same may be said of the moon, obliged to follow the earth.
And this may serve for those simple ones who have difficulty in
comprehending how these two globes, not being chained together, nor
strung upon a pole, mutually follow each other, so that on the
acceleration or retardation of the one, the other also moves quicker or
slower."
The second Dialogue is appropriated chiefly to the discussion of the
diurnal motion of the earth; and the principal arguments urged by
Aristotle, Ptolemy, and others, are successively brought forward and
confuted. The opposers of the earth's diurnal motion maintained, that if
it were turning round, a stone dropped from the top of a tower would not
fall at its foot; but, by the rotation of the earth to the eastward
carrying away the tower with it, would be left at a great distance to
the westward; it was common to compare this effect to a stone dropped
from the mast-head of a ship, and without any regard to truth it was
boldly asserted that this would fall considerably nearer the stern than
the foot of the mast, if the ship were in rapid motion. The same
argument was presented in a variety of forms,—such as that a
cannon-ball shot perpendicularly upwards would not fall at the same
spot; that if fired to the eastward it would fly farther than to the
westward; that a mark to the east or west would never be hit, because of
the rising or sinking of the horizon during the flight of the ball; that
ladies' ringlets would all stand out to the westward,[102] with other
conceits of the like nature: to which the general reply is given, that
in all these cases the stone, or ball, or other body, participates
equally in the motion of the earth, which, therefore, so far as regards
the relative motion of its parts, may be disregarded. The manner in
which this is illustrated, appears in the following extract from the
dialogue:—"_Sagredo._ If the nib of a writing pen which was in the ship
during my voyage direct from Venice to Alexandria, had had the power of
leaving a visible mark of all its path, what trace, what mark, what line
would it have left?—_Simplicio._ It would have left a line stretched
out thither from Venice not perfectly straight, or to speak more
correctly, not perfectly extended in an exact circular arc, but here and
there more and less curved accordingly as the vessel had pitched more or
less; but this variation in some places of one or two yards to the right
or left, or up or down in a length of many hundred miles, would have
occasioned but slight alteration in the whole course of the line, so
that it would have been hardly sensible, and without any great error we
may speak of it as a perfectly circular arc.—_Sagred._ So that the true
and most exact motion of the point of the pen would also have been a
perfect arc of a circle if the motion of the vessel, abstracting from
the fluctuations of the waves, had been steady and gentle; and if I had
held this pen constantly in my hand, and had merely moved it an inch or
two one way or the other, what alteration would that have made in the
true and principal motion?—_Simpl._ Less than that which would be
occasioned in a line a thousand yards long, by varying here and there
from perfect straightness by the quantity of a flea's eye.—_Sagred._ If
then a painter on our quitting the port had begun to draw with this pen
on paper, and had continued his drawing till we got to Alexandria, he
would have been able by its motion, to produce an accurate
representation of many objects perfectly shadowed, and filled up on all
sides with landscapes, buildings, and animals, although all the true,
real, and essential motion of the point of his pen would have been no
other but a very long and very simple line; and as to the peculiar work
of the painter, he would have drawn it exactly the same if the ship had
stood still. Therefore, of the very protracted motion of the pen, there
remain no other traces than those marks drawn upon the paper, the reason
of this being that the great motion from Venice to Alexandria was common
to the paper, the pen, and everything that was in the ship; but the
trifling motion forwards and backwards, to the right and left,
communicated by the painter's fingers to the pen, and not to the paper,
from being peculiar to the pen, left its mark upon the paper, which as
to this motion was immoveable. Thus it is likewise true that in the
supposition of the earth's rotation, the motion of a falling stone is
really a long track of many hundreds and thousands of yards; and if it
could have delineated its course in the calm air, or on any other
surface, it would have left behind it a very long transversal line; but
that part of all this motion which is common to the stone, the tower,
and ourselves, is imperceptible by us and the same as if not existing,
and only that part remains to be observed of which neither we nor the
tower partake, which in short is the fall of the stone along the tower."
The mechanical doctrines introduced into this second dialogue will be
noticed on another occasion; we shall pass on to other extracts,
illustrative of the general character of Galileo's reasoning:—
"_Salviati._ I did not say that the earth has no principle, either
internal or external, of its motion of rotation, but I do say that I
know not which of the two it has, and that my ignorance has no power to
take its motion away; but if this author knows by what principle other
mundane bodies, of the motion of which we are certain, are turned round,
I say that what moves the Earth is something like that by which Mars and
Jupiter, and, as he believes, the starry sphere, are moved round; and if
he will satisfy me as to the cause of their motion, I bind myself to be
able to tell him what moves the earth. Nay more; I undertake to do the
same if he can teach me what it is which moves the parts of the earth
downwards.—_Simpl._ The cause of this effect is notorious, and every
one knows that it is Gravity.—_Salv._ You are out, Master Simplicio;
you should say that every one knows that it is called Gravity; but I do
not ask you the name but the nature of the thing, of which nature you do
not know one tittle more than you know of the nature of the moving cause
of the rotation of the stars, except it be the name which has been given
to the one, and made familiar and domestic, by the frequent experience
we have of it many thousand times in a day; but of the principle or
virtue by which a stone falls to the ground, we really know no more than
we know of the principle which carries it upwards when thrown into the
air, or which carries the moon round its orbit, except, as I have said,
the name of gravity which we have peculiarly and exclusively assigned to
it; whereas we speak of the other with a more generic term, and talk of
the virtue impressed, and call it either an assisting or an informing
intelligence, and are content to say that Nature is the cause of an
infinite number of other motions."
Simplicio is made to quote a passage from Scheiner's book of Conclusions
against Copernicus, to the following effect:—"'If the whole earth and
water were annihilated, no hail or rain would fall from the clouds, but
would only be naturally carried round in a circle, nor would any fire or
fiery thing ascend, since, according to the not improbable opinion of
these others, there is no fire in the upper regions.'—_Salv._ The
foresight of this philosopher is most admirable and praiseworthy, for he
is not content with providing for things that might happen during the
common course of nature, but persists in shewing his care for the
consequences of what he very well knows will never come to pass.
Nevertheless, for the sake of hearing some of his notable conceits, I
will grant that if the earth and water were annihilated there would be
no more hail or rain, nor would fiery matter ascend any more, but would
continue a motion of revolution. What is to follow? What conclusion is
the philosopher going to draw?—_Simpl._ This objection is in the very
next words—'Which nevertheless (says he) is contrary to experience and
reason.'—_Salv._ Now I must yield: since he has so great an advantage
over me as experience, with which I am quite unprovided. For hitherto I
have never happened to see the terrestrial earth and water annihilated,
so as to be able to observe what the hail and fire did in the confusion.
But does he tell us for our information at least what they did?—_Simp._
No, he does not say any thing more.—_Salv._ I would give something to
have a word or two with this person, to ask him whether, when this globe
vanished, it also carried away the common centre of gravity, as I fancy
it did, in which case I take it that the hail and water would remain
stupid and confounded amongst the clouds, without knowing what to do
with themselves.... And lastly, that I may give this philosopher a less
equivocal answer, I tell him that I know as much of what would follow
after the annihilation of the terrestrial globe, as he could have known
what was about to happen in and about it, before it was created."
Great part of the third Dialogue is taken up with discussions on the
parallax of the new stars of 1572 and 1604, in which Delambre notices
that Galileo does not employ logarithms in his calculations, although
their use had been known since Napier discovered them in 1616: the
dialogue then turns to the annual motion "first taken from the Sun and
conferred upon the Earth by Aristarchus Samius, and afterwards by
Copernicus." Salviati speaks of his contemporary philosophers with great
contempt—"If you had ever been worn out as I have been many and many a
time with hearing what sort of stuff is sufficient to make the obstinate
vulgar unpersuadable, I do not say to agree with, but even to listen to
these novelties, I believe your wonder at finding so few followers of
these opinions would greatly fall off. But little regard in my judgment
is to be had of those understandings who are convinced and immoveably
persuaded of the fixedness of the earth, by seeing that they are not
able to breakfast this morning at Constantinople, and sup in the evening
in Japan, and who feel satisfied that the earth, so heavy as it is,
cannot climb up above the sun, and then come tumbling in a breakneck
fashion down again!"[103] This remark serves to introduce several
specious arguments against the annual motion of the earth, which are
successively confuted, and it is shewn how readily the apparent stations
and retrogradations of the planets are accounted for on this
supposition.
The following is one of the frequently recurring passages in which
Galileo, whilst arguing in favour of the enormous distances at which the
theory of Copernicus necessarily placed the fixed stars, inveighs
against the arrogance with which men pretend to judge of matters removed
above their comprehension. "_Simpl._ All this is very well, and it is
not to be denied that the heavens may surpass in bigness the capacity of
our imaginations, as also that God might have created it yet a thousand
times larger than it really is, but we ought not to admit anything to be
created in vain, and useless in the universe. Now whilst we see this
beautiful arrangement of the planets, disposed round the earth at
distances proportioned to the effects they are to produce on us for our
benefit, to what purpose should a vast vacancy be afterwards interposed
between the orbit of Saturn and the starry spheres, containing not a
single star, and altogether useless and unprofitable? to what end? for
whose use and advantage?—_Salv._ Methinks we arrogate too much to
ourselves, Simplicio, when we will have it that the care of us alone is
the adequate and sufficient work and bound, beyond which the divine
wisdom and power does and disposes of nothing. I feel confident that
nothing is omitted by the Divine Providence of what concerns the
government of human affairs; but that there may not be other things in
the universe dependant upon His supreme wisdom, I cannot for myself, by
what my reason holds out to me, bring myself to believe. So that when I
am told of the uselessness of an immense space interposed between the
orbits of the planets and the fixed stars, empty and valueless, I reply
that there is temerity in attempting by feeble reason to judge the works
of God, and in calling vain and superfluous every part of the universe
which is of no use to us.—_Sagr._ Say rather, and I believe you would
say better, that we have no means of knowing what is of use to us; and I
hold it to be one of the greatest pieces of arrogance and folly that can
be in this world to say, because I know not of what use Jupiter or
Saturn are to me, that therefore these planets are superfluous; nay
more, that there are no such things in nature. To understand what effect
is worked upon us by this or that heavenly body (since you will have it
that all their use must have a reference to us), it would be necessary
to remove it for a while, and then the effect which I find no longer
produced in me, I may say that it depended upon that star. Besides, who
will dare say that the space which they call too vast and useless
between Saturn and the fixed stars is void of other bodies belonging to
the universe. Must it be so because we do not see them: then I suppose
the four Medicean planets, and the companions of Saturn, came into the
heavens when we first began to see them, and not before! and, by the
same rule, the other innumerable fixed stars did not exist before men
saw them. The nebulæ were till lately only white flakes, till with the
telescope we have made of them constellations of bright and beautiful
stars. Oh presumptuous! rather, Oh rash ignorance of man!"
After a discussion on Gilbert's Theory of Terrestrial Magnetism,
introduced by the parallelism of the earth's axis, and of which Galileo
praises very highly both the method and results, the dialogue proceeds
as follows:—"_Simpl._ It appears to me that Sig. Salviati, with a fine
circumlocution, has so clearly explained the cause of these effects,
that any common understanding, even though unacquainted with science,
may comprehend it: but we, confining ourselves to the terms of art,
reduce the cause of these and other similar natural phenomena to
sympathy, which is a certain agreement and mutual appetency arising
between things which have the same qualities, just as, on the other
hand, that disagreement and aversion, with which other things naturally
repel and abhor each other, we style antipathy.—_Sagr._ And thus with
these two words they are able to give a reason for the great number of
effects and accidents which we see, not without admiration, to be
produced in Nature. But it strikes me that this mode of philosophising
has a great sympathy with the style in which one of my friends used to
paint: on one part of the canvas he would write with chalk—there I will
have a fountain, with Diana and her nymphs; here some harriers; in this
corner I will have a huntsman, with a stag's head; the rest may be a
landscape of wood and mountain; and what remains to be done may be put
in by the colourman: and thus he flattered himself that he had painted
the story of Actæon, having contributed nothing to it beyond the names."
The fourth Dialogue is devoted entirely to an examination of the tides,
and is a development and extension of the treatise already mentioned to
have been sent to the Archduke Leopold, in 1618.[104] Galileo was
uncommonly partial to his theory of the tides, from which he thought to
derive a direct proof of the earth's motion in her orbit; and although
his theory was erroneous, it required a farther advance in the science
of motion than had been attained even at a much later period to point
out the insufficiency of it. It is well known that the problem of
explaining the cause of this alternate motion of the waters had been
considered from the earliest ages one of the most difficult that could
be proposed, and the solutions with which different inquirers were
obliged to rest contented, shew that it long deserved the name given to
it, of "the grave of human curiosity."[105] Riccioli has enumerated
several of the opinions which in turn had their favourers and
supporters. One party supposed the rise of the waters to be occasioned
by the influx of rivers into the sea; others compared the earth to a
large animal, of which the tides indicated the respiration; a third
theory supposed the existence of subterraneous fires, by which the sea
was periodically made to boil; others attributed the cause of a similar
change of temperature to the sun and moon.
There is an unfounded legend, that Aristotle drowned himself in despair
of being able to invent a plausible explanation of the extraordinary
tides in the Euripus. His curiosity on the subject does not appear to
have been so acute (judging from his writings) as this story would
imply. In one of his books he merely mentions a rumour, that there are
great elevations or swellings of the seas, which recur periodically,
according to the course of the moon. Lalande, in the fourth volume of
his Astronomy, has given an interesting account of the opinion of the
connection of the tides with the moon's motion. Pytheas of Marseilles, a
contemporary of Aristotle, was the first who has been recorded as
observing, that the full tides occur at full moon, and the ebbs at new
moon.[106] This is not quite correctly stated; for the tide of new moon
is known to be still higher than the rise at the full, but it is likely
enough, that the seeming inaccuracy should be attributed, not to
Pytheas, but to his biographer Plutarch, who, in many instances,
appears to have viewed the opinions of the old philosophers through the
mist of his own prejudices and imperfect information. The fact is, that,
on the same day when the tide rises highest, it also ebbs lowest; and
Pytheas, who, according to Pliny, had recorded a tide in Britain of
eighty cubits, could not have been ignorant of this. Posidonius, as
quoted by Strabo, maintained the existence of three periods of the tide,
daily, monthly, and annual, "in sympathy with the moon."[107] Pliny, in
his vast collection of natural observations, not unaptly styled the
Encyclopædia of the Antients, has the following curious passages:—"The
flow and ebb of the tide is very wonderful; it happens in a variety of
ways, but the cause is in the sun and moon."[108] He then very
accurately describes the course of the tide during a revolution of the
moon, and adds: "The flow takes place every day at a different hour;
being waited on by the star, which rises every day in a different place
from that of the day before, and with greedy draught drags the seas with
it."[109] "When the moon is in the north, and further removed from the
earth, the tides are more gentle than when digressing to the south, she
exerts her force with a closer effort."[110]
The College of Jesuits at Coimbra appears to deserve the credit of first
clearly pointing out the true relation between the tides and the moon,
which was also maintained a few years later by Antonio de Dominis and
Kepler. In the Society's commentary on Aristotle's book on Meteors,
after refuting the notion that the tides are caused by the light of the
sun and moon, they say, "It appears more probable to us, without any
rarefaction, of which there appears no need or indication, that the moon
raises the waters by some inherent power of impulsion, in the same
manner as a magnet moves iron; and according to its different aspects
and approaches to the sea, and the obtuse or acute angles of its
bearing, at one time to attract and raise the waters along the shore,
and then again to leave them to sink down by their own weight, and to
gather into a lower level."[111] The theory of Universal Gravitation
seems here within the grasp of these philosophers, but unfortunately it
did not occur to them that possibly the same attraction might be exerted
on the earth as well as the water, and that the tide was merely an
effect of the diminution of force, owing to the increase of distance,
with which the centre of the earth is attracted, as compared with that
exerted on its surface. This idea, so happily seized afterwards by
Newton, might at once have furnished them with a satisfactory
explanation of the tide, which is observed on the opposite side of the
earth as well as immediately under the moon. They might have seen that
in the latter case the centre of the earth is pulled away from the
water, just as in the former the water is pulled away from the centre of
the earth, the sensible effect to us being in both cases precisely the
same. For want of this generalization, the inferior tide as it is called
presented a formidable obstacle to this theory, and the most plausible
explanation that was given was, that this magnetic virtue radiated out
from the moon was reflected by the solid heavens, and concentrated again
as in a focus on the opposite side of the earth. The majority of modern
astronomers who did not admit the existence of any solid matter fit for
producing the effect assigned to it, found a reasonable difficulty in
acquiescing in this explanation. Galileo, who mentions the Archbishop of
Spalatro's book, treated the theory of attraction by the moon as absurd.
"This motion of the seas is local and sensible, made in an immense mass
of water, and cannot be brought to obey light, and warmth, and
predominancy of occult qualities, and such like vain fancies; all which
are so far from being the cause of the tide, that on the contrary the
tide is the cause of them, inasmuch as it gives rise to these ideas in
brains which are more apt for talkativeness and ostentation, than for
speculation and inquiry into the secrets of Nature; who, rather than see
themselves driven to pronounce these wise, ingenuous, and modest
words—_I do not know_,—will blurt out from their tongues and pens all
sorts of extravagancies."
Galileo's own theory is introduced by the following illustration, which
indeed probably suggested it, as he was in the habit of suffering no
natural phenomena, however trivial in appearance, to escape him. He felt
the advantage of this custom in being furnished on all occasions with a
stock of homely illustrations, to which the daily experience of his
hearers readily assented, and which he could shew to be identical in
principle with the phenomena under discussion. That he was mistaken in
applying his observations in the present instance cannot be urged
against the incalculable value of such a habit.
"We may explain and render sensible these effects by the example of one
of those barks which come continually from Lizza Fusina, with fresh
water for the use of the city of Venice. Let us suppose one of these
barks to come thence with moderate velocity along the canal, carrying
gently the water with which it is filled, and then, either by touching
the bottom, or from some other hindrance which is opposed to it, let it
be notably retarded; the water will not on that account lose like the
bark the impetus it has already acquired, but will forthwith run on
towards the prow where it will sensibly rise, and be depressed at the
stern. If on the contrary the said vessel in the middle of its steady
course shall receive a new and sensible increase of velocity, the
contained water before giving into it will persevere for some time in
its slowness, and will be left behind that is to say towards the stern
where consequently it will rise, and sink at the head.—Now, my masters,
that which the vessel does in respect of the water contained in it, and
that which the water does in respect of the vessel containing it, is the
same to a hair as what the Mediterranean vase does in respect of the
water which it contains, and that the waters do in respect of the
Mediterranean vase which contains them. We have now only to demonstrate
how, and in what manner it is true that the Mediterranean, and all other
gulfs, and in short all the parts of the earth move with a motion
sensibly not uniform, although no motion results thence to the whole
globe which is not perfectly uniform and regular."
This unequable motion is derived from a combination of the earth's
motion on her axis, and in her orbit, the consequence of which is that a
point under the sun is carried in the same direction by the annual and
diurnal velocities, whereas a point on the opposite side of the globe is
carried in opposite directions by the annual and diurnal motions, so
that in every twenty-four hours the absolute motion through space of
every point in the earth completes a cycle of varying swiftness. Those
readers who are unacquainted with the mathematical theory of motion must
be satisfied with the assurance that this specious representation is
fallacious, and that the oscillation of the water does not in the least
result from the causes here assigned to it: the reasoning necessary to
prove this is not elementary enough to be introduced here with
propriety.
Besides the principal daily oscillation of the water, there is a monthly
inequality in the rise and fall, of which the extremes are called the
spring and neap tides: the manner in which Galileo attempted to bring
his theory to bear upon these phenomena is exceedingly curious.
"It is a natural and necessary truth, that if a body be made to revolve,
the time of revolution will be greater in a greater circle than in a
less: this is universally allowed, and fully confirmed by experiments,
such for instance as these:—In wheel clocks, especially in large ones,
to regulate the going, the workmen fit up a bar capable of revolving
horizontally, and fasten two leaden weights to the ends of it; and if
the clock goes too slow, by merely approaching these weights somewhat
towards the centre of the bar, they make its vibrations more frequent,
at which time they are moving in smaller circles than before.[112]—Or,
if you fasten a weight to a cord which you pass round a pulley in the
ceiling, and whilst the weight is vibrating draw in the cord towards
you, the vibrations will become sensibly accelerated as the length of
the string diminishes. We may observe the same rule to hold among the
celestial motions of the planets, of which we have a ready instance in
the Medicean planets, which revolve in such short periods round Jupiter.
We may therefore safely conclude, that if the moon for instance shall
continue to be forced round by the same moving power, and were to move
in a smaller circle, it would shorten the time of its revolution. Now
this very thing happens in fact to the moon, which I have just advanced
on a supposition. Let us call to mind that we have already concluded
with Copernicus, that it is impossible to separate the moon from the
earth, round which without doubt it moves in a month: we must also
remember that the globe of the earth, accompanied always by the moon,
revolves in the great circle round the sun in a year, in which time the
moon revolves round the earth about thirteen times, whence it follows
that the moon is sometimes near the sun, that is to say between the
earth and sun, sometimes far from it, when she is on the outside of the
earth. Now if it be true that the power which moves the earth and the
moon round the sun remains of the same efficacy, and if it be true that
the same moveable, acted on by the same force, passes over similar arcs
of circles in a time which is least when the circle is smallest, we are
forced to the conclusion that at new moon, when in conjunction with the
sun, the moon passes over greater arcs of the orbit round the sun, than
when in opposition at full moon; and this inequality of the moon will be
shared by the earth also. So that exactly the same thing happens as in
the balance of the clocks; for the moon here represents the leaden
weight, which at one time is fixed at a greater distance from the centre
to make the vibrations slower, and at another time nearer to accelerate
them."
Wallis adopted and improved this theory in a paper which he inserted in
the Philosophical Transactions for 1666, in which he declares, that the
circular motion round the sun should be considered as taking place at a
point which is the centre of gravity of the earth and moon. "To the
first objection, that it appears not how two bodies that have no tie can
have one common centre of gravity, I shall only answer, that it is
harder to show how they have it, than that they have it."[113] As Wallis
was perfectly competent from the time at which he lived, and his
knowledge of the farthest advances of science in his time, to appreciate
the value of Galileo's writings, we shall conclude this chapter with the
judgment that he has passed upon them in the same paper. "Since Galileo,
and after him Torricelli and others have applied mechanical principles
to the solving of philosophical difficulties, natural philosophy is well
known to have been rendered more intelligible, and to have made a much
greater progress in less than a hundred years than before for many
ages."
FOOTNOTES:
[93] See page 56.
[94] Playfair's Dissertation, Supp. Encyc. Brit.
[95] Astronomia Nova. Pragæ. 1609.
[96] The new Planet no Planet, or the Earth no wandering Star, except in
the wandering heads of Galileans. London, 1646.
[97] Aristarchi Samii de Mundi Systemate. Parisiis 1644.
[98] See page 12.
[99] De Cœlo, lib. iv. cap. 3.
[100] Reflexiones Physico-Mathematicæ, Parisiis, 1647.
[101] Venturi.
[102] Riccioli.
[103] The notions commonly entertained of 'up' and 'down,' as connected
with the observer's own situation, had long been a stumbling-block in
the way of the new doctrines. When Columbus held out the certainty of
arriving in India by sailing to the westward on account of the earth's
roundness, it was gravely objected, that it might be well enough to sail
down to India, but that the chief difficulty would consist in climbing
up back again.
[104] See page 50.
[105] Riccioli Almag. Nov.
[106] Plutarch, De placit. Philos. lib. iii. c. 17.
[107] συμπαθεως τῃ σεληνη. Geographiæ, lib. iii.
[108] Historia Naturalis, lib. ii. c, 97.
[109] Ut ancillante sidere, trahenteque secum avido haustu maria.
[110] Eâdem Aquiloniâ, et à terris longius recedente, mitiores quam cum,
in Austros digressâ, propiore nisu vim suam exercet.
[111] Commentarii Collegii Conimbricensis. Coloniæ, 1603.
[112] See fig. 1. p. 96.
[113] Phil. Trans., No. 16, August 1666.