SAGREDO.
I do not know whether you are really arriving later than usual for our
accustomed discussion or whether it just seems so to me because of my
desire to hear Salviati's thoughts on such an interesting matter. I
have been watching through the window for a long time, hoping from one
moment to the next to see the gondola come into view which I sent to
fetch you.
SALV. I believe it is only your
imagination that has made the time drag, rather than any tardiness on
our part. But in order not to stretch it still further it will be good
for us to get to the matter in hand without wasting any more words.
Let us see, then, how nature has allowed
(whether the facts are actually such, or whether at a whim and as if to
play upon our fancies) -- has allowed, I say, the movements that have
long been attributed to the earth for every reason except as an
explanation of the ocean tides to be found now to serve that purpose
too, with equal precision; and how, reciprocally, this ebb and flow
itself cooperates in confirming. the earth's mobility. Up to this point
the indications of that mobility have been taken from celestial
phenomena, seeing that nothing which takes place on the earth has been
powerful enough to establish the one position any more than the other.
This we have already examined at length by showing that all terrestrial
events from which it is ordinarily held that the earth stands still and
the sun and the fixed stars are moving would necessarily appear just
the same to us if the earth moved and the others stood still. Among all
sublunary things it is only in the element of water (as something which
is very vast and is not joined and linked with the terrestrial. globe
as are all its solid parts, but is rather, because of its fluidity,
free and separate and a law unto itself) that we may recognize some
trace or indication of the earth's behavior in regard to motion and
rest. After having many times examined for myself the effects and
events, partly seen and partly heard ; from other people, which are
observed in the movements of the water; after, moreover, having read
and listened to the great follies which many people have put forth as
causes for these events, I have arrived at two conclusions which were
not lightly to be drawn and granted. Certain necessary assumptions
having been made, these are that if the terrestrial globe were
immovable, the ebb and flow of the oceans could not occur naturally;
and that when we confer upon the globe the movements just assigned to
it, the seas are necessarily subjected to an ebb and flow agreeing in
all respects with what is to be observed in them.
SAGR. The proposition is crucial,
both in itself and in what follows as a consequence; therefore I shall
be so much the more attentive in listening to its explanation and
verification.
SALV. In questions of natural science
like this one at hand, I a knowledge of the effects is what leads to an
investigation and discovery of the causes. Without this, ours would be
a blind journey, or one even more uncertain than that; for we should
not know where we wanted to come out, whereas the blind at least know
where they wish to arrive. Hence before all else it is necessary to
have a knowledge of the effects whose causes we are seeking. Of those
effects you, Sagredo, must be more fully and surely informed than I am,
since besides being born in Venice and having long resided here where
the tides are famous for their size, you have also sailed to Syria,
and, having a clever and curious mind, you must have made many
observations. But I, who have only been able to observe for rather a
short time what happens here at this end of the Adriatic Gulf, and in
our lower sea on the shores of the Tyrrhenian, must often depend upon
what others tell me -- which, being for the most part not in good
agreement and accordingly rather unreliable, may contribute confusion
rather than confirmation to our reflections.
Still, from those accounts which we are sure
of, and which happen to cover the principal events, it seems to me
possible to arrive at the true and primary causes. I do not presume to
be able to adduce all the proper and sufficient causes of those effects
which are new to me and which consequently I have had no chance to
think about; what I am about to say, I propose merely as a key to open
portals to a road never before trodden by anyone, in a firm hope that
minds more acute than mine will broaden this road and penetrate further
along it than I have done in my first revealing of it. And though in
other seas remote from us events may take place which do not occur in
our Mediterranean, nevertheless the reason and the cause which I shall
produce will still be true, provided that it is verified and fully
satisfied by the events which do take place in our sea; for ultimately
one single true and primary cause must hold good for effects which are
similar in kind. I shall, then, tell you the story of the effects which
I know to exist, and assign to them the cause that is believed by me to
be true; and you, gentlemen, shall produce others noticed by you in
addition to these of mine, and then we shall see whether the cause I am
about to adduce can account for them also.
I say, then, that three periods are observed
in the flow and ebb of the ocean waters. The first and principal one is
the great and conspicuous daily tide, in accordance with which the
waters rise and fall at intervals of some hours; these intervals in the
Mediterranean are for the most part about six hours each -- that is,
six hours of rising and six more of falling. The second period is
monthly, and seems to originate from the motion of the moon; it does
not introduce other movements, but merely alters the magnitude of those
already mentioned, with a striking difference according as the moon is
full, new, or at quadrature with the sun. The third period is annual,
and appears to depend upon the sun; it also merely alters the daily
movements by rendering them of different sizes at the solstices from
those occurring at the equinoxes.
We shall speak first about the diurnal
period, as it is the principal one, and the one upon which the actions
of the moon and the sun are exercised secondarily in their monthly and
annual alterations. Three varieties of these hourly changes are
observed; in some places the waters rise and fall without making any
forward motion; in others, without rising or falling they move now
toward the east and again run back toward the west; and in still
others, the height and the course both vary. This occurs here in
Venice, where the waters rise in entering and fall in departing. They
do this at the end of a gulf extending east I and west and terminating
on open shores where the water '. has room to spread out upon rising;
if their course were interrupted by mountains or by very high dikes,
they would rise and sink against these without any forward motion.
Elsewhere the water runs to and fro in its central parts without
changing height, as happens notably in the Straits of Messina between
Scylla and Charybdis, where the currents are very swift because of the
narrowness of the channel. But in the open Mediterranean and around its
islands, such as the Balearics, Corsica, Sardinia, Elba, Sicily (on the
African side), Malta, Crete, etc., the alterations of height are very
small but the currents are quite noticeable, especially where the sea
is restrained between islands, or between these and the continent.
Now it seems to me that these actual and
known effects alone, even if no others were to be seen, would very
probably persuade anyone of the mobility of the earth who is willing to
stay within the bounds of nature; for to hold fast the basin of the
Mediterranean and to make the water contained within it behave as it
does surpasses my imagination, and perhaps that of anyone else who
enters more than superficially into these reflections.
SIMP. These events, Salviati, did not
just commence; they are very ancient, and have been observed by
innumerable men, many of whom have contrived to give one reason or
another to account for them. Not far from here there is a great
Peripatetic who gives for them a cause recently dredged out of one of
Aristotle's texts which had not been well understood by his
interpreters. From this text, he deduces that the true cause of these
movements stems from nothing else but the various depths of the seas.
The deepest waters, being more abundant and therefore heavier, . expel
the waters of lesser depth; these, being raised up, then try to
descend, and from this continual strife the tides are derived.
Then there are many who refer the tides to
the moon, saying that this has a particular dominion over the water.
Lately a certain prelate has published a little tract wherein he says
that the moon, wandering through the sky, attracts and draws up toward
itself a heap of water which goes along following it, so that the high
sea is always in that part which lies under the moon. And since when
the moon is below the horizon, this rising nevertheless returns, he
tells us that he can say nothing to account for this effect except that
the moon not only retains this faculty naturally in itself, but in this
case has also the power to confer it upon the opposite sign of the
zodiac. Others, as I think you know, say that the moon also has power
to rarefy the water by its temperate heat, and that thus rarefied, it
is lifted up. Nor are those lacking who . . .
SAGR. Please, Simplicio, spare us the
rest; I do not think there is any profit in spending the time to
recount them, let alone the words to refute them. If you should give
assent to any of these or to similar triflings, you would be wronging
your own judgment -- just when, as we know, it has been, much
unburdened of error.
SALV. I am a little more easygoing
than you, Sagredo, and I shall put in a few words for Simplicio's
benefit if he thinks that some probability attaches to the things he
has been telling us.
Simplicio, I say that waters which have
their external surfaces higher expel those that are lower, but not that
those which are deeper do so; and the higher waters, having driven away
the lower, quickly come to rest and equilibrium. Your Peripatetic must
believe that all the lakes in the world (which remain placid) and all
the seas where the tide is imperceptible must have perfectly level
beds; I was so naIve as to persuade myself that even if there were no
other soundings, the Islands whIch rise above the water would be a very
obvious indication of the unevenness of the bottoms. You might tell
your prelate that the moon travels over the whole Mediterranean every
day, but the waters are raised only at its eastern extremity and for us
here at Venice.
As for those who make the temperate heat of
the moon able to swell the water, you may tell them to put afire under
a kettle of water, hold their right hands in this until I the heat
raises the water a single inch, and then take them out to write about
the swelling of the seas. Or ask them at least to show you how the moon
rarefies a certain part. of the water and not the remainder, such as
this here at Venice, but not that at Ancona, Naples, or Genoa.
Let us just say that there are two sorts of
poetical minds -- one kind apt at inventing fables, and the other
disposed to believe them.
SIMP. I do not think that anyone
believes fables when he knows them to be such; and as to the opinions
about the cause of the tides (which are numerous), since I know that
there is only one true and primary cause for one effect, I understand
perfectly that at most one can be true, and all the rest must be false
and fabulous. Perhaps the true one is not even among those which have
been produced up to date. I rather believe this to be so, since it
would be remarkable if the true cause should shed so little light as
not to show through the darkness of so many false ones. But I must say,
with that frankness which is permitted here among ourselves, that to
introduce the motion of the earth and make it the cause of the tides
seems to me thus far to be a concept no less fictitious than all the
rest I have heard. If no reasons more agreeable to natural phenomena
were presented to me, I should pass on unhesitatingly to the belief
that the tide is a supernatural effect, and accordingly miraculous and
inscrutable to the human mind -- as are so many others which depend
directly upon the omnipotent hand of God.
SALV. You argue very prudently, and
also in agreement with Aristotle's doctrine; at the beginning of his
Mechanics; as you know, he ascribes to miracles all things whose causes
are hidden. But I believe you do not have any stronger indication that
the true cause of the tides is one of : those incomprehensibles than
the mere fact that among all I things so far adduced as verae causae
there is not one which we can duplicate for ourselves by means of
appropriate artificial devices. For neither by the light of the moon or
sun, nor by temperate heat, nor by differences of depth can we ever
make the water contained in a motionless vessel run to and fro, or rise
and fall in but a single place. But if, by simply setting the vessel in
motion, I can represent for you without any artifice at all precisely
those changes which are perceived in the waters of the sea, why should
you reject this cause and take refuge in miracles?
SIMP. I shall have recourse to
miracles unless you dissuade me from it by other natural causes than
the motion of the containers of the waters of the sea. For I know that
the latter containers do not move, the entire terrestrial globe being
naturally immovable.
SALV. But do you not believe that the
terrestrial globe could be made movable supernaturally, by God's
absolute power?
SIMP. Who can doubt this?
SALV. Then, Simplicio, since we must
introduce a miracle to achieve the ebbing and flowing of the oceans,
let us make the earth miraculously move with that motion by which the
oceans are naturally moved. This operation will indeed be as much
simpler and more natural among things miraculous, as it is easier to
make a globe turn around (which we see so many of them do) than to make
an immense bulk of water go back and forth more rapidly in some places
than in others; rise and fall, here more, there less, and in other
places not at all, and to make all these variations within the same
containing vessel. Besides, these are many miracles, while the other is
only one. Add to this that the miracle of making the water move brings
another miracle in its train, which ,is that of holding the earth
steady against the impulses of the water. For these would be capable of
making it vacillate first in one direction and then in the other, if it
were not miraculously retained.
SAGR. Let us suspend judgment for a
while as to the folly of the new opinion which Salviati wants to
explain to us, Simplicio, and not be so quick to class it with those
ridiculous older ones. As to the miracle, let us likewise have recourse
to that only after we have heard arguments which are restricted within
the bounds of nature. Though, indeed, to my mind all works of nature
and of God appear miraculous.
SALV. That is the way I feel about
it, and saying that the natural cause of the tides is the motion of the
earth does not exclude this operation from being miraculous.
Now, returning to our discussion, I reply
and reaffirm that it has never previously been known how the waters
contained in our Mediterranean basin can make those movements which
they are seen to make, so long as this basin and containing vessel
rests motionless. What renders the matter puzzling is daily observed,
as I am about to describe; therefore, listen carefully.
We are here in Venice, where the waters are
now low; the sea is quiet, the air tranquil; the water is commencing to
rise, and at the end of five or six hours it will have gone up ten
spans or more. This rise is not made by the original water being
rarefied, but by water newly arriving here -- water of the same kind as
the original water, with the same salinity, the same density, the same
weight. Ships float in it, Simplicio, without submerging a
hair's-breadth further; a barrel of it weighs not a grain more or less
than the same quantity of the other; it keeps the same coldness
entirely unchanged; in short, it is water which has recently and
visibly entered through the channels and mouths of the Lido.
Now you tell me how and whence it came here.
Are there perchance hereabouts some abysses or openings in the bottom
of the sea through which the earth draws in and expels the water,
breathing like some immense and monstrous whale? If so, why does the
water not rise likewise over a space of six hours at Ancona, Dubrovnik
(Ragugia), and Corfu, where the increase is small or even
imperceptible? Who will find a way to pour new water into an immovable
vessel and have it rise only in one definite place and not in others?
Do you perhaps say that this new water is
borrowed from the ocean, carried in through the Straits of Gibraltar?
This will not remove the difficulties mentioned; it will only make them
greater. In the first place, tell me what must be the course of that
water which, entering by the strait, is conducted in six hours clear to
the extreme coast of the Mediterranean, a distance of tWo or three
thousand miles, and retraces the same space on its retUrn? What would
become of the ships scattered about on the sea? And what of those in
the strait, on a continual watery precipice of immense bulk, entering
through a channel no more than eight miles wide -- a channel which must
in six hours give passage to enough water to inundate a space hundreds
of miles wide and thousands long? Where is the tiger or falcon that
ever ran or flew with such speed? A speed, I mean, of 400 miles an hour
or better.
It cannot be denied that there are currents
running the length of the gulf, but they are so slow that a rowboat can
outrun them, though not without losing headway. Besides, if this water
comes in through the strait, there is another difficulty: How does it
cause so much of a rise here, at so remote a place, without first
raising the closer parts by a similar or greater amount? To sum up, I
do not believe that either obstinacy or subtleness of wit could ever
discover a reply to these difficulties and thereby be able to maintain
the fixity of the earth against them, while remaining within natural
limitations.
SAGR. So far I follow you very well,
and I am anxiously waiting to hear how these marvels can take place
unimpeded if we assume the motions already assigned to the earth.
SALV. As these effects must be
consequences of the motions which belong naturally to the earth it is
not only necessary that they encounter no obstacle or impediment, but
that they follow easily. Nor must they merely follow easily; they must
follow necessarily, in such a way that it would be impossible for them
to take place in any other manner For such is the property and
condition of things which are natural and true.
Having established, then, that it is
impossible to explain the movements perceived in the waters and at the
same time maintain the immovability of the vessel which contains them,
let us pass on to considering whether the mobility of the container
could produce the required effect in I the way in which it is observed
to take place. Two sorts of .movement may be conferred upon a vessel so
that the : water contained in it acquires the property of running first
I toward one end and then toward the other, and rise and , sink there.
The first would occur when one end is lowered I and then the other, for
under those conditions the water, ~ running toward the depressed part,
rises and sinks alternately at either end. But since this rising and
sinking is I nothing but a retreat from and an approach toward the
center of the earth, this sort of movement cannot be attributed to
concavities in the earth itself as containing vessels of the waters,
For such containers could not have parts I able to approach toward or
retreat from the center of the ~ terrestrial globe by any motion
whatever that might be assigned to the latter.
The other sort of motion would occur when
the vessel was moved without being tilted, advancing not uniformly but
with a changing velocity, being sometimes accelerated and sometimes
retarded. From this variation it would follow that the water (being
contained within the vessel but not firmly adhering to it as do its
solid parts) would because of its fluidity be almost separate and free,
and not compelled to follow all the changes of its container. Thus the
vessel being retarded, the water would retain apart of the impetus
already received, so that it would run toward the forward end, where it
would necessarily rise. On the other hand, when the vessel was speeded
up, the water would retain apart of its slowness and would fall
somewhat behind while becoming accustomed to the new impetus, remaining
toward the back end, where it would rise somewhat.
These effects can be very clearly explained
and made evident to the senses by means of the example of those barges
which are continually arriving from Fusina filled with water for the
use of this city. Let us imagine to ourselves such a barge coming along
the lagoon with moderate speed, placidly carrying the water with which
it is filled, when either by running aground or by striking some
obstacle it becomes greatly retarded. Now the water will not thereby
lose its previously received impetus equally with the barge; keeping
its impetus, it will run forward toward the prow, where it will rise
perceptibly, sinking at the stern. But if on the other hand the same
barge noticeably increases its speed in the midst of its placid course,
then the water which it contains (before getting used to this and while
retaining its slowness) will stay back toward the stern, where it will
consequently rise, sinking at the prow. This effect is indubitable and
clear; it may be tested experimentally at any time, and there are three
things about it which I want you to note particularly.
The first is that in order to make the water
rise at one extremity of the vessel, there is no need of new water, nor
need the water run there from the other end.
The second is that the water near the middle
does not rise or sink noticeably unless the course of the barge happens
to be very fast to begin with, and the object struck or other hindrance
which checks it is very strong and unyielding. In such an event this
might not only make all the water run forward, but cause most of it to
jump right out of the barge; the same would also happen if a very
violent impulse were suddenly given to it when it was traveling very
slowly. But if to a gentle motion of its own there were added a
moderate retardation or acceleration, the parts in the middle (as I
said) would rise and sink imperceptibly, and the other parts would rise
the less according as they were closer to the middle, and the more
according as they were farther from it.
The third thing is that whereas the parts
around the center make little change as to rising or sinking with
respect to the water at the ends, yet they run to and fro a great deal
in comparison with the water at the extremities.
Now, gentlemen, what the barge does with
regard to the water it contains, and what the water does with respect
to the barge containing it, is precisely the same as what the
Mediterranean basin does with regard to the water contained within it,
and what the water contained does with respect to the Mediterranean
basin, its container. The next thing is for us to prove that it is
true, and in what manner it is true, that the Mediterranean and all
other sea basins (in a word, that all parts of the earth) move with a
conspicuously uneven motion, even though nothing but regular and
uniform motions may happen to be assigned to the globe itself.
SIMP. At first sight this looks like
a great paradox to me, though I am no mathematician or astronomer. If
it is true that the motion of the whole maybe regular, and that of the
parts which always remain attached to it may be irregular, then this is
a paradox destroying the axiom which affirms tandem esse rationem
totius et partium.
SALV. I shall prove my paradox,
Simplicio, and then leave to you the burden of either defending the
axiom against it or of bringing the two into accord. My demonstration
will be brief and easy; it will depend upon things already dealt with
at length in our past conversations, without introducing the slightest
word to make it favor the ebb and flow.
We have already said that there are two
motions attributed to the terrestrial globe; the
first is annual, made by its center along the circumference of its
orbit about the ecliptic in the order of D the signs of the zodiac
(that is, from west to east), and the other is made by the globe itself
revolving around its own center in twenty-four hours (likewise from
west to east) around an axis which is somewhat tilted, and not parallel
to that of its annual revolution. From the composition of these two
motions, each of them in itself uniform, I say that there results an
uneven motion in the parts of the earth. In order for this to be
understood more easily, I shall explain it by drawing a diagram.
First I shall describe around the center A
the circumference of the earth's orbit BC, on which the point B is
taken; and around this as center, let us describe this smaller circle
DEFG, representing the terrestrial globe. We shall suppose that its
center B runs along the whole circumference of the orbit from west to
east; that is, from B toward C. We shall further suppose the
terrestrial globe to turn around its own center B from west to east, in
the order of the points D, E, F, G, during a period of twenty-four
hours. Now here we must carefully note that when a circle revolves
around its own center, every part of it must move at different times
with contrary motions. This is obvious, considering that when the part
of the circumference around the point D is moving toward the left
(toward E), the opposite parts, around F, go toward the right (toward
G); so that when the point D gets to F, its motion will be contrary to
what it was originally when it was at D. Moreover, in the same time
that the point E descends, so to speak, toward F, G ascends toward D.
Since this contrariety exists in the motion of the parts of the
terrestrial surface when it is turning around its own center, it must
happen that in coupling the diurnal motion with the annual, there
results an absolute motion of the parts of the surface which is at one
time very much accelerated and at another retarded by the same amount.
This is evident from considering first the parts around D, whose
absolute motion will be very swift, resulting from two motions made in
the same direction; that is, toward the left. The first of these is
part of the annual motion, common to all parts of the globe; the other
is that of this same point D, carried also to the left by the diurnal
whirling, so that in this case the diurnal motion increases and
accelerates the annual motion.
It is quite the opposite with the part
across from D, at F. This, while the common annual motion is carrying
it toward the left together with the whole globe, is carried to the
right by the diurnal rotation, so that the diurnal motion detracts from
the annual. In this way the absolute motion -- the resultant of the
composition of these tw0 is much retarded.
Around the points E and G, the absolute
motion remains equal to the simple annual motion, since the diurnal
motion acts upon it little or not at all, tending neither to left nor
to right, but downward and upward. From this we conclude that just as
it is true that the motion of the whole globe and of each of its parts
would be equable and uniform if it were moved with a single motion,
whether this happened to be the annual or the diurnal, so is it
necessary that upon these two motions being mixed together there
results in the parts of the globe this uneven motion, now accelerated
and now retarded by the additions and subtractions of the diurnal
rotation upon the annual revolution.
Now if it is true (as is indeed proved by
experience) that the acceleration and retardation of motion of a vessel
makes the contained water run back and forth along its length, and rise
and fall at its extremities, then who will make any trouble about
granting that such an effect may -- or rather, must -- take place in
the ocean waters? For their basins are subjected to just such
alterations; especially those which extend from west to east, in which
direction the movement of these basins is made.
Now this is the most fundamental and
effective cause of the tides, without which they would not take place.
But the particular events observed at different times and places are
many and varied; these must depend upon diverse concomitant causes,
though all must have some connection with the fundamental cause. So our
next business is to bring up and examine the different phenomena which
may be the causes of such diverse effects.
The first of these is that whenever the
water, thanks to some considerable retardation or acceleration of
motion of its containing vessel, has acquired a cause for running
toward one end or the other, it will not remain in that state when the
primary cause has ceased. For by virtue of its own weight and its
natural inclination to level and balance itself, it will speedily
return of its own accord; and being heavy and fluid, it will not only
return to equilibrium but will pass beyond it, pushed by its own
impetus, and will rise at the end where first it sank. But it will not
stay there; , by repeated oscillations of travel it will make known to
us that it does not want the speed of motion it has received to be
suddenly removed and reduced to a state of rest. It wishes this to be
slowly reduced, abating little by little. In exactly this way we see
that a weight suspended by a cord, once removed from the state of rest
(that is, the perpendicular), returns to this and comes to rest by
itself, but only after having gone to and fro many times, passing
beyond this perpendicular position in its coming and going.
The second event to be noticed is that the
reciprocations of movement just mentioned are made and repeated with
greater or less frequency (that is, in shorter or longer times)
according to the various lengths of the vessels containing the water.
In the shorter space, the reciprocations are more frequent, and they
are rarer in the longer, just as in the above example of the plumb bobs
the reciprocations of those which are hung on long cords are seen to be
less frequent than those hanging from shorter threads.
For the third remark, you must know that it
is not only a greater or lesser length of vessel which causes the water
to perform its reciprocations in different times, but a greater or less
depth does the same thing. It happens that for water contained in
vessels of equal length but of unequal depth, the deeper water will
make its vibrations in briefer times, and the oscillations will be less
frequent in the shallower.
Fourth, such vibrations produce two effects
in water which are worthy of being noticed and observed carefully. One
is the alternating rising and falling at either extremity; the other is
the horizontal moving and running to and fro, so to speak. These two
different motions inhere differently in different parts of the water,
The extreme ends of the water rise and fall the most; the central parts
do not move, up and down at all; and other parts, by degrees as they
are nearer to the ends, rise and fall proportionately more than .those
farther from the ends. On the other hand, the central parts move a
great deal in that other (progressive) movement back and forth, going
and returning, while the waters in the extreme ends have none of this
motion -- except so far as they may in rising happen to go higher than
their banks, and spill out of their original channel and container. But
where the hindrance of the banks restrains them, they merely rise and
fall; nor does this prevent the waters in the middle from running back
and forth, as do the other parts in proportion, traveling the more or
the less according as they are located farther from or closer to the
middle.
The fifth particular event must be more
carefully considered, because it is impossible for us to duplicate its
effects by any practical experiment. It is this: In an artificial
vessel like the barge mentioned previously, moving now more rapidly and
again more slowly, the acceleration or retardation is always shared
uniformly by the whole vessel and by each of its parts. Thus, for
example, when the barge is checked in its motion, its forward parts are
no more retarded than its after parts, but all share equally in the
same retardation. The same happens in acceleration; that is, conferring
some new cause of greater velocity upon the barge accelerates the bow
in the same way as the stern. But in immense vessels, such as long sea
bottoms (though these indeed are nothing more than cavities made in the
solidity of the terrestrial globe), it nevertheless happens remarkably
enough that their extremities do not increase and decrease in speed
jointly, equally, and in the same instant of time. For it may happen
that when one extremity of such a vessel is greatly retarded in its
motion by virtue of a composition of these two motions, annual and
diurnal, the other extremity may be affected by and involved in even a
very swift motion. For your easier comprehension, let us explain this
by going back to the diagram previously drawn. Let us suppose a stretch
of sea to be as long as one quadrant; the arc BC, for instance. Then
the parts near B are, as I said before, in very swift motion because
the two movements (annual and diurnal) are united in the same
direction, and the parts near C are at that time in retarded motion,
since they lack the forward movement depending upon the diurnal motion.
If we suppose, I
say, a sea bottom as long as the arc BC, we shall see at once that its
extremities are moving very unequally at a given time. A stretch of sea
as long as a semicircle and placed in the position of the arc BCD will
have exceedingly different speeds, since the extremity B would be in
very rapid motion, Din very slow motion, and the parts in the middle
around C in moderate motion. In proportion as these stretches of sea
were shorter, they would participate less in this strange phenomenon of
having their parts diversely affected at certain times of day by speed
and by slowness of motion.
Now if in the first place we see
experimentally that an acceleration and a retardation shared equally by
all parts of the containing vessel may indeed be the cause of the
contained water running back and forth, then what must we suppose would
happen in a vessel so remarkably situated that a retardation and an
acceleration of motion are conferred very unevenly upon its parts?
Certainly we cannot help saying that there would necessarily be
perceived still greater and more marvelous causes of commotions in the
water, and stranger ones. And though to many people it may seem
impossible for us to test the effects of such events in artificial
devices and vessels, nevertheless this is not entirely impossible; I
have a mechanical model in which the effects of these marvelous
compositions of movements may be observed in detail. But so far as our
present purpose is concerned, what we have grasped intellectually up to
this point is sufficient.
SAGR. For my part, I understand well
enough that this remarkable phenomenon must necessarily exist in the
ocean beds, especially in those which extend a long distance east and
west; that is, along the direction of the movements of the terrestrial
globe. And as the phenomenon is in a certain sense undreamed of and
without parallel among the movements it is possible for us to make, it
is not hard for me to believe that it may produce effects which cannot
be imitated in our artificial experiments.
SALV. These things being cleared up,
it is now time to examine in all their diversity the particular events
which are observed experientially in the ebbing and flowing of the
waters. First, it cannot be hard for us to understand why it happens
that in lakes, pools, and even in small seas there is no noticeable
tide. There are two impelling reasons for this. One is that because of
the shortness of their basins they acquire at different hours of the
day varying degrees of speed, but with little difference occurring
among all their parts; they are uniformly accelerated and retarded as
much in front as behind; that is, to the east as to the west. And they
acquire such alterations, moreover, little by little, and not through
the opposition of a sudden obstacle and hindrance, or a sudden and
great acceleration in the movement of the containing vessel. The
latter, with all its parts, becomes slowly and equally impressed with
the same degree of velocity, and from this uniformity it follows that
the contained water also receives the same impressions with little
resistance or hesitation. Consequently the signs of rising and falling
or of running to one extremity or the other are exhibited only
obscurely. This effect is also clearly seen in small artificial
vessels, in which the contained water is impressed with the same
degrees of speed, whenever the acceleration or retardation is made in
slow and uniform increments. But in the basins of oceans which extend a
great distance from east to west, the acceleration or retardation is
much more noticeable and uneven when one extremity of them is in a very
retarded motion and the other is moving quickly.
The second reason is the reciprocal
oscillation of the water instituted by the impetus already received
from the motion of its container, which oscillation (as we have
remarked) makes its vibrations with high frequency in small vessels.
There inheres in the terrestrial movements a cause for conferring a
movement upon the waters only from one twelve-hour period to another,
since only once a day is the movement of the containing vessel
exceedingly accelerated or retarded.. Now this second cause depends
upon the weight of the water, which seeks to restore it to equilibrium,
and it produces oscillations of one, two, or three hours, and so on,
according to the shortness of the vessel. Thus the whole movement
becomes entirely insensible upon this one being combined with the
first, which even by itself remains very small for small vessels. For
the primary cause, which has a period of twelve hours, will not have
finished impressing its disturbance when overtaken and reversed by this
second one depending upon the weight of the water and having a
vibration time of one, two, three, or four hours, and so on, according
to the shortness and depth of the basin. Acting contrary to the first
cause, this perturbs and removes that without ever allowing it to
attain the height, or even the average of its motion. Any evidence of
ebbing or flowing is entirely annihilated by this conflict, or is very
much obscured. I say nothing of the continual changing of the wind,
which by disquieting the water would not permit us to be sure of some
very small rising or falling, of half an inch or less, which might
actually belong to the basins and containers of bodies of water no more
than one degree or so in length.
Now, secondly, I shall resolve the question
why, since there resides in the primary principle no cause of moving
the waters except from one twelve-hour period to another (that is, once
by the maximum speed of motion and once by its maximum slowness), the
period of ebbing and flowing nevertheless commonly appears to be from
one six-hour period to another. Such a determination, I say, can in no
way come from the primary cause alone. The secondary causes must be
introduced for it; that is, the greater or lesser length of the vessels
and the greater or lesser depth of the waters contained in them. These
causes, although they do not operate to move the waters (that action
being from the primary cause alone, without which there would be no
tides), are nevertheless the principal factors in limiting the duration
of the reciprocations, and operate so powerfully that the primary cause
must bow to them. Six hours, then, is not a more proper or natural
period for these reciprocations than any other interval of time, though
perhaps it has been the one most generally observed because it is that
of our Mediterranean, which has been the only place practicable for
making observations over many centuries. Even so, this period is not
observed everywhere in it; in some of the narrower places, such as the
Hellespont and the Aegean, the periods are much briefer, and they are
also quite variable among themselves. Some say it was because of these
differences and the incomprehensibility of their causes to Aristotle
that he, after observing them for a long time from some cliffs of
Euboea (Negroponte), plunged into the sea in a fit of despair and
willfully destroyed himself.
In the third place we shall see very readily
the reason why a sea like the Red Sea, although very long, is
nevertheless quite devoid of any tide. This is so because its length
does not extend from east to west, but runs from southeast to
northwest. The movements of the earth being from west to east, the
impulses of the water are always aimed against the meridians and not
from one parallel to another. Hence in seas which extend lengthwise
toward the poles and are narrow in the other direction, there is no
cause of tides -- unless it is that of sharing those of some other sea
with which they may communicate and which is subject to large
movements.
We can very easily understand, in the fourth
place, the reasons why the ebbing and flowing are greatest at the
extremities of gulfs as to rising and falling of the waters, and least
in the middle parts. Daily experience shows us this here in Venice,
sitUated at the end of the Adriatic, where the difference commonly
amounts to as much as five or six feet; but in parts of the
Mediterranean distant from the extremities such changes are very small;
as at the islands of Corsica and Sardinia, and on the coasts at Rome
and Leghorn, where they do not exceed half a foot. We understand also
why, on the other hand, where the rising and falling are small, the
running to and fro is large. It is a simple thing, I say, to understand
the cause of these events, because we have examples of them easily
observable in all sorts of artificially manufactured vessels, in which
the same effects are seen to follow naturally when we move them
unevenly; that is, now accelerating and now retarding them.
Let us consider further, in the fifth place,
how a given quantity of water moving slowly in a spacious channel must
run very impetuously when it has to pass through a narrow place. From
this we shall have no difficulty in understanding the cause of the
great current which is created in the narrow channel that separates
Calabria from Sicily. For all the water pent up by the extensive island
and the Ionian Gulf in the eastern part of the sea, though because of
the spaciousness there it descends slowly toward the west, yet upon
being restrained in the Straits of Messina between Scylla and
Charybdis, it drops rapidly and makes a great agitation. Something
similar to this, but greater, is said to occur between Africa and the
great island of Madagascar (San Lorenzo), when the waters of the two
great Indian and South Atlantic (Etiopico) oceans, in whose midst this
lies, must be restricted in their running into the still smaller
channel between it and the coast of South Africa. The currents in the
Straits of Magellan must be extremely great, communicating between the
South Atlantic and the South Pacific oceans.
In the sixth place, in order to give reasons
for some more recondite and curious events that are observed in this
field, it remains now for us to make another important reflection upon
the two principal causes of the tides, thereafter compounding them and
mixing them together. The first and simplest of these, as I .have often
said, is the definite acceleration and retardation of the parts of the
earth from which the waters receive a determinate period, running
toward the east and returning to the west within a space of twenty-four
hours. The other depends upon the water's own weight, which, once moved
by the primary cause, tries then to restore itself to equilibrium by
repeated oscillations which are not determinate as to one
preestablished time alone, but which have differences of duration
according to the different lengths and depths of the containers and
basins of the oceans. In so far as they depend upon this second
principle, some would flow and return in one hour, some in two, in
four, in six, in eight, in ten, etc.
Now if we commence to add the first cause,
which has an established period of twelve hours, to the second when it
has for example a period of five, then it will sometimes happen that
the primary and secondary causes agree in making their impulses both in
the same direction; and in such a conjunction ( or, so to speak, in
such a unanimous conspiracy) the tides will be very great. At other
times it happens that the primary impulse becomes in a certain sense
contrary to that brought by the secondary; and in such encounters one
impulse takes away what the other gives, so that the motion of the
waters is weakened and the sea is reduced to a very peaceful and
practically motionless state. At still other times, when the two
principles are not in opposition nor yet entirely unified, they cause
other variations in the rise and fall of the tides.
It may also happen that two very large seas
which are in communication through some narrow channel are found to
have, because of the mixture of the two principles of motion, a cause
of flood in one at the very time the other is having the contrary
movement. In this case extraordinary agitations are made in the channel
through which they communicate, with opposing motions and vortexes and
most dangerous churnings, of which in fact we hear continual tales and
accounts. From such discordant movements, depending not only upon
different situations and lengths, but even more upon the differing
depths of the communicating seas, there sometimes arise various
disorderly and unobservable aquatic commotions whose causes have
perturbed sailors very much, and still do, when encountered in the
absence either of gusts of wind or other significant atmospheric
changes which might account for them.
Now these disturbances of the air must be
carefully taken into consideration with the other phenomena, and
regarded as a third occasional cause capable of greatly altering our
observations of effects dependent upon the primary and more essential
causes. For there is no doubt that strong winds blowing continuously
from the east, for instance, may sustain the waters, preventing their
ebb. If then a second recurrence of the high tide, and even a third, is
added at the established hours, the waters will swell up very high. In
such away, sustained for several days by the force of the wind, they
may be raised much more than usual, and make extraordinary floods. We
must also take notice of another cause of movement, and this will be
our seventh problem. This depends upon the great quantity of water from
the rivers that empty into seas which are not vast, for which reason
the water is seen to run always in the same direction in channels or
straits through which such seas communicate, as happens in the Thracian
Bosporus below Constantinople, where the water runs always from the
Black Sea toward the Sea of Marmara (Propontide). For the Black Sea the
principal causes of ebb and flow are not very effective, because of its
shortness; while on the other hand very large rivers empty into it, and
this great flow of water must be passed and disgorged through the
strait, where the current is quite famous and is always toward the
south. Moreover, we must take note that this strait or channel, though
it is certainly very narrow, is not subjected to any such perturbations
as the strait between Scylla and Charybdis; for the former has the
Black Sea above it to the north, with the Sea of Marmara, the Aegean
Sea, and the Mediterranean adjoining it to the south -- though over a
long tract, and, as we have already noted, however long a sea may be
from north to south, it is not subject to tides. But since the Sicilian
strait is situated between parts of the Mediterranean, extending a
great distance from west to east -- that is, with the tidal currents --
the agitations in it are very great. They would be still greater at the
Gates of Hercules, if the Straits of Gibraltar were less open; and the
currents in the Straits of Magellan are reported to be extremely
strong.
This is all that occurs to me at present to
tell you about the causes of this basic diurnal period of the tides,
and of their various incidental phenomena. If anything is to be brought
up in connection with these, it may be done now; then we may proceed to
the other two periods, the monthly and the annual.
SIMP. I do not think it can be denied
that your argument goes along very plausibly, the reasoning being ex
suppositions, as we say; that is, assuming that the earth does move in
the two motions assigned to it by Copernicus. But if we exclude these
movements, all the rest is vain and invalid; and the exclusion of this
hypothesis is very clearly pointed out to us by your own reasoning.
Under the assumption of the two terrestrial movements, you give reasons
for the ebbing and flowing; and vice versa, arguing circularly, you
draw from the ebbing and flowing the sign and confirmation of those
same two movements. Passing to a more specific argument, you say that
on account of the water being a fluid body and not firmly attached to
the earth, it is not rigorously constrained to obey all the earth's
movements. From this you deduce its ebbing and flowing.
In your own footsteps, I argue the contrary
and say: The air is even more tenuous and fluid than the water, and
less affixed to the earth's surface, to which the water adheres (if for
no other reason) because of its own weight, which presses its own much
more than the very light air. Then so much the less should the air
follow the movements of the earth; hence if the earth did move in those
ways, we, its inhabitants, carried along at the same velocity, would
have to feel a wind from the east perpetually beating against us with
intolerable force. That such would necessarily follow, daily experience
informs us; for if, in riding post with no more speed than eight or ten
miles an hour in still air, we feel in our faces what resembles a wind
blowing against us not lightly, just think what our rapid course of
eight hundred or a thousand miles per hour would have to produce
against air which was free from such motion! Yet we feel nothing of any
such phenomenon.
SALV. To this objection, which seems
so persuasive, I reply that it is true that the air is much more
tenuous and much lighter than the water, and by its lightness is much
less adherent to the earth than heavy and bulky water. But the
consequence which you deduce from these conditions is false; that is,
that because of its lightness, tenuity, and lesser adherence to the
earth it must be freer than water from following the movements of the
earth, so that to us who participate completely in those movements its
disobedience would be made sensible and evident. In fact, quite the
opposite happens. For if you will remember carefully, the cause of the
ebbing and flowing of the water assigned by us consisted in the water
not following the irregularity of motion of its vessel, but retaining
the impetus which it had previously received, and not diminishing it or
increasing it in the exact amount by which this is increased or
diminished in the vessel. Now since disobedience to a new increase or
diminution of motion consists in conservation of the original received
impetus, that moving body which is best suited for such conservation
will also be best fitted for exhibiting the effect that follows as a
consequence of this conservation. How strongly water is disposed to
preserve a disturbance once received, even after the cause impressing
it has ceased to act, is demonstrated I to us by the experience of
water highly agitated by strong winds. Though the winds may have ceased
and the airs become tranquil, such waves remain in motion for along
time, as the sacred poet so charmingly sings: Qual l'alto Egeo, etc.
The continuance of the commotion in this way depends upon the weight of
the water, for as has been said on other occasions, light bodies are
indeed much easier to set in motion than heavier ones, but they are
also much less able to keep the motion impressed upon them, once the
cause of motion stops. The air, being a thing that is in itself very
tenuous and extremely light, is most easily movable by the slightest
force; but it is also most inept at conserving the motion when the
mover ceases acting.
As to the air that surrounds the terrestrial
globe, I shall therefore say that it is carried around by its adherence
no less than the water, and especially those parts of it which are
contained in vessels, these vessels being plains surrounded by
mountains. And we may much more reasonably declare that such parts are
carried around, swept along by the roughness of the earth, than that
the higher parts are swept along by the celestial motion as the
Peripatetics assert.
What I have said so far seems to me to be an
adequate reply to Simplicio's objection. But I want to give him more
than satisfaction by means of a new objection and another reply,
founded upon a remarkable experiment, and at the same time substantiate
for Sagredo the mobility of the earth.
I have said that the air, and especially
that part of it which is not above the highest mountains, is carried
around by the roughness of the earth's surface. From this it seems to
follow that if the earth were not uneven, but smooth and polished,
there would be no reason for its taking the air along as company, or at
least for its conducting it with so much uniformity. Now the surface of
this globe of ours is not all mountainous and rough, but there are very
large areas that are quite smooth; such are the surfaces of the great
oceans. These, being also quite distant from the mountain ranges that
encirc1e them, appear not to have any aptitude for carrying along the
air above them; and whatever may follow as a consequence of not
carrying it ought therefore to be felt in such places.
SIMP. I also wanted to raise this
same objection, which seems to me very powerful.
SALV. You may well say this,
Simplicio, in the sense that from no such thing being felt in the air
as would result from this globe of ours going around, you argue its
immobility. But what if this thing that you think ought to be felt as a
necessary consequence were, as a matter of fact, actually felt? Would
you accept this as a sign and a very powerful argument of the mobility
of this same globe?
SIMP. In that case it would not be a
matter of dealing with me alone; for if this should happen and its
cause were hidden from me, perhaps it might be known to others.
SALV. So no one can ever win against
you, but must always lose; then it would be better not to play.
Nevertheless, in order not to cheat our umpire, I shall go on.
We have just said, and will now repeat with
some additions, that the air, as a tenuous and fluid body which is not
solidly attached to the earth, seems to have no need of obeying the
earth's motion, except in so far as the roughness of the terrestrial
surface catches and carries along with it that part of the air which is
contiguous to it, or does not exceed by any great distance the greatest
altitude of the mountains. This portion of the air ought to be least
resistant to the earth's rotation, being filled with vapors, fumes, and
exhalations, which are materials that participate in the earthy
properties and are consequently naturally adapted to these same
movements. But where the cause for motion is lacking -- that is, where
the earth's surface has large flat spaces and where there would be less
admixture of earthy vapors -- the reason for the surrounding air to
obey entirely the seizure of the terrestrial rotation would be partly
removed. Hence, while the earth is revolving toward the east, a beating
wind blowing from east to west ought to be continually felt in such
places, and this blowing should be most perceptible where the earth
whirls most rapidly; this would be in the places most distant from the
poles and closest to the great circle of the diurnal rotation.
Now the fact is that actual experience
strongly confirms this philosophical argument. For within the Torrid
Zone (that is, between the tropics), in the open seas, at those w parts
of them remote from land, just where earthy vapors are absent, a
perpetual breeze is felt moving from the east with so constant a tenor
that, thanks to this, ships prosper in their voyages to the West
Indies. Similarly, departing from the Mexican coast, they plow the
waves of the Pacific Ocean with the same ease toward the East Indies,
which are east to us but west to them. On the other hand, voyages from
the Indies eastward are difficult and uncertain, nor may they in any
case be made along the same routes, but must be piloted more toward the
land so as to find other occasional and variable winds caused by other
principles, such as we dwellers upon terra firma continually
experience. There are many and various reasons for the origin of such
winds which we need not bother to bring up at present. These occasional
winds blow indifferently toward all f parts of the earth, disturbing
seas distant from the equator and bordered by the rough surface of the
earth. This amounts to saying that such seas are subjected to those
disturbances of the air which interfere with the primary current of air
that would be felt continually, especially on the ocean, if such
accidental disturbances were lacking.
Now you see how the actions of the water and
the air show themselves to be remarkably in accord with celestial
observations in confirming the mobility of our terrestrial globe.
SAGR. Yet in order to cap all this, I
wish also to tell you one particular which seems to me to be unknown to
you, yet which confirms this same conclusion. You, Salviati, have
mentioned that phenomenon which sailors encounter in the tropics; I
mean that constant wind blowing from the east, of which I have heard
accounts from those who have made the voyage quite often. Moreover, it
is an interesting fact that sailors do not call this a "wind," but have
some other name for it which slips my mind, taken perhaps from its even
tenor. When they encounter it, they tie up their shrouds and the other
cordage of the sails, and without ever again having any need to touch
these, they can continue their voyage in security, or even asleep. Now
this perpetual breeze has been known and recognized by reason of its
blowing continuously without interruption; for if other winds had
interrupted it, it would not have been recognized as a singular effect
different from all the others. From this I may infer that the
Mediterranean Sea might also participate in such a phenomenon, but that
this escapes unobserved because it is frequently interrupted by other
supervening winds. I say this advisedly, and upon very probable
theories which occurred to me from what I had occasion to learn during
the voyage I made to Syria when I went to Aleppo as consul of our
nation. Keeping a special record and account of the days of departure
and arrival of ships at the ports of Alexandria, Alexandretta, and here
at Venice, I discovered in these again and again that, to my great
interest, the returns here (that is, the voyages from east to west over
the Mediterranean) were made in proportionately less time than those in
the opposite direction, in a ratio of 25 per cent. Thus we see that on
the whole the east winds are stronger than those from the west.
SA LV. I am glad to know of this detail,
which contributes not a little confirmation to the mobility of the
earth. And though it may be said that all the water of the
Mediterranean pours perpetually through the Straits of Gibraltar,
having to disgorge into the ocean all the waters of so many rivers that
empty into it, I do not believe that the current can be so strong that
it alone could make such a remarkable difference. This is also evident
from seeing that the water at Pharos runs back toward the east no less
than it courses toward the west.
SAGR. I, who unlike Simplicio, have
not been worrying about convincing anybody besides myself, am satisfied
with what has been said regarding this first part. Therefore, Salviati,
if you wish to proceed, I am ready to listen.
SALV. I am yours to command; but I
should like to hear also how it looks to Simplicio, for from his
judgment I can estimate how much I may expect from these arguments of
mine in the Peripatetic schools, should they ever reach those ears.
SIMP. I do not want you to take my
opinion asa basis for guessing at the judgments of others. As I have
often said, I am among the tyros in this sort of study, and things
which would occur to those who have penetrated into the profoundest
depths of philosophy might never occur to me; for, as the saying goes,
I have hardly greeted its doorkeeper. Yet to show some spark of fire, I
shall say that as for the effects recounted by you, and this last one
in particular, it seems possible to me to render quite sufficient
reasons from the mobility of the heavens alone, without introducing any
novelties beyond the mere converse of what you yourself have brought
into the field.
It is admitted by the Peripatetic school
that the element of fire and a large part of the air are carried around
in the diurnal rotation from east to west by contact with the lunar
sphere as their containing vessel. Now without deviating from your
footprints, I should like us to establish the quantity of air
participating in that motion as that part which ~ comes down about to
the summits of the highest mountains, and would extend on down to the
earth itself if the obstacle presented by these very mountains did not
hinder it. Thus, just as you declared that the air surrounding the
mountain ranges is carried around by the roughness of the moving earth,
we say the converse-- that all the element of air is carried around by
the motion of the heavens except that part which is lower than the
mountain peaks, this being impeded by the roughness of the immovable
earth. And where you would say that if such roughness were removed,
this would also free the air from being caught, we may say that if this
roughness were removed, all the air I would proceed in this movement.
And since the surfaces of the open seas are smooth and level, the
motion of the breeze which blows perpetually from the east continues
there, and is more noticeable at places near the equator, within the
tropics, where the motion of the heavens is most rapid.
And as this celestial movement is powerful
enough to carry the free air with it, we may say quite reasonably that
it contributes this same motion to the movable water. For this is
fluid, and unattached to the earth's immobility. We may affirm this
with the more confidence in view of your own admission that such a
movement need be only very small with respect to its effective cause,
which, going around the entire terrestrial globe in one natural day;
passes over many thousands of miles per hour (especially near the
equator), while currents in the open sea move but a very few miles per
hour. In this way our voyages toward the west would be much more
convenient and rapid, being assisted not only by the perpetual eastern
breeze, but also by the course of the waters.
Perhaps from that same coursing of the
water, tides also may arise; the water, striking against the variously
situated shores, might even return straight back in the opposite
direction, as experience shows us in the courses of rivers. For there
the water, because of the irregularity of the banks, often meets some
part which juts out or which makes a hollow from beneath, and it whirls
around and is seen to return perceptibly. Hence it seems to me that the
same effects from which you argue the mobility of the earth (and which
mobility you offer as a cause for them) may be sufficiently explained
if we hold the earth fixed and restore the mobility to the heavens.
SALV. It cannot be denied that your
argument is ingenious and carries something of probability, but I say
that this is a probability in appearance only and not in reality. There
are two parts to your argument; in the first, you render a reason for
the continual motion of the eastern breeze, and also for the motion of
the water; in the second, you wish also to obtain a cause for the tides
from the same source. The first part, as I have said, has some
semblance of probability, though much less than we achieve from
terrestrial motion. The second part is not only entirely improbable,
but is absolutely impossible and false.
As to the first, in which you say that the
hollow of the lunar sphere sweeps along with it the element of fire and
all the air down to the summits of the highest mountains, I say first
that there is doubt whether any element of fire exists. Even assuming
that it does, it is extremely doubtful whether the lunar sphere exists;
or indeed, whether any of the other "spheres" do. That is to say, it is
questionable whether there actually are such bodies, solid and
extremely vast, or whether beyond the air there does not rather extend
a continuous expanse of a substance very much more tenuous and pure
than our air, and whether the planets do not wander through this, as is
now commencing to be held even by most of these same philosophers.
But however that may be, there is no reason
for us to believe that fire, by simple contact with a surface which you
yourself consider to be remarkably smooth and even, should in its
entire extent be carried around in a motion foreign to its own
inclination. This has been proved throughout II Saggiatore, and
demonstrated by sensible experiments. Beyond this, there is the further
improbability of such motions being transferred from most subtle fire
to the air, which is much denser, and then from this to water.
But that a body of very rough and
mountainous surface, by revolving, should conduct along with it the
contiguous air which strikes against its prominences is not merely
probable, but necessary; it may be seen from experience, although I
believe that even without seeing it no one would cast doubt upon it.
As for the rest, assuming that the air and
even the water were conducted by the motion of the heavens, such a
motion would have nothing whatever to do with the tides. For since from
one uniform cause only one single uniform effect can follow, there
would have to be discovered in the waters a continual and uniform
current from east to west, existing only in those oceans which,
returning upon themselves, encircle the globe. In inland seas such as
the Mediterranean, hemmed in as it is on the east, there could be no
such motion. For if its waters were driven by the course of the heavens
toward the west, it would have been dried up many centuries ago;
besides which, our waters do not run only toward the west, but return
back toward the east in regular periods. If indeed you should say, from
the example of the rivers, that the course of the seas was originally
from east to west only, but that the different situations of their
shores might force some of the water to flow in reverse, then I shall
grant you this, Simplicio; but you must take note that wherever the
water is moved back for this reason, it perpetually returns again,
while where it runs forward, it always keeps going in the same
direction, as you may see from your example of the rivers. As to the
tides, you must discover and bring forth reasons for making them run
now one way and now the other at the same place--effects which, being
contrary and irregular, you can never deduce from one uniform and
constant cause. This, as well as overthrowing the idea of a motion
being contributed to the sea by the diurnal movement of the heavens,
also defeats those who would like to grant to the earth only the
diurnal motion and who believe that with this alone they can give a
reason for the tides. For since the effect is irregular, it is
necessarily required that its causes shall be irregular and variable.
SIMP. I have nothing further to say;
neither on my own account, because of my lack of inventiveness, nor on
that of others, because of the novelty of the opinion. But I do indeed
believe that if this were broadcast among the schools, there would be
no lack of philosophers who would be able to cast doubt upon it.
SAGR. Then let us wait until that
happens. In the meantime, if it is satisfactory with you, Salviati, let
us proceed.
SALV. Everything that has been said
up to this point pertains to the diurnal period of the tides, of which
the primary and universal cause has first been proved, without which no
effect whatever would take place. Next, passing on to the particular
events to be observed in this diurnal period (which vary and are in a
certain sense irregular), the secondary and concomitant causes upon
which these depend remain to be dealt with.
Now two other periods occur, the monthly and
the annual. These do not introduce new and different events beyond
those already considered under the diurnal period, but they act upon
the latter by making them greater or less at different parts of the
lunar month and at different seasons of the solar year -- almost as
though the moon and sun were taking part in the production of such
effects. But that concept is completely repugnant to my mind; for
seeing how this movement of the oceans is a local and sensible one,
made in an immense bulk of water, I cannot bring myself to give
credence to such causes as lights, warm temperatures, predominances of
occult qualities, and similar idle imaginings. These are so far from
being actual or possible causes of the tides that the very contrary is
true. The tides are the cause of them; that is, make them occur to
mentalities better equipped for loquacity and ostentation than for
reflections upon and investigations into the most hidden works of
nature. Rather than be reduced to offering those wise, clever, and
modest words, "I do not know," they hasten to wag their tongues and
even their pens in the wildest absurdities.
We see that the moon and the sun do not act
upon small receptacles of water by means of light, motion, and great or
moderate heat; rather, we see that to make water rise by heat, one must
bring it almost to boiling. In short, we cannot artificially imitate
the movement of the tides in any way except by movement of the vessel.
Now should not these observations assure anyone that all the other
things produced as a cause of this effect are vain fantasies, entirely
foreign to the truth of the matter?
Thus I say that if it is true that one
effect can have only one basic cause, and if between the cause and the
effect there is a fixed and constant connection, then whenever a fixed
and constant alteration is seen in the effect, there must be a fixed
and constant variation in the cause. Now since the alterations which
take place in the tides at different times of the year and of the month
have their fixed and constant periods, it must be that regular changes
occur simultaneously in the primary cause of the tides. Next, the
alterations in the tides at the said times consist of nothing more than
changes in their sizes; that is, in the rising and lowering of the
water a greater or less amount, and its running with greater or less
impetus. Hence it is necessary that whatever the primary cause of the
tides is, it should increase or diminish its force at the specific
times mentioned. But it has already been concluded that an irregularity
and unevenness in the motion of the vessel containing the water is the
primary cause of the tides; therefore this unevenness must become
correspondingly still more irregular from time to time (that is, must
increase or diminish).
Now we must remember that the unevenness
(that is, the varying velocity of the vessels which are parts of the
earth's surface) depends upon these vessels moving with a composite
motion, the resultant of compounding the annual and the diurnal motions
which belong to the entire terrestrial globe. Of these the diurnal
whirling, with its alternate addition to and subtraction from the
annual movement, is the thing that produces the unevenness of the
compound motion. Thus the primary cause of the uneven motion of the
vessels, and hence of that of the tides, consists in the additions and
subtractions which the diurnal whirling makes with respect to the
annual motion. And if these additions and subtractions were always made
in the same proportion with respect to the annual motion, the cause of
tides would indeed continue to exist, but only a cause for their being
perpetually made in the same manner. Now we must find a reason for
these same tides being made greater and less at different times; hence,
if we wish to preserve the identity of the cause, there is a necessity
of finding changes in these additions and subtractions, making them
more and less potent at producing those effects which depend upon them.
But I do not see how this can be done accept by making these additions
and subtractions, now greater and now less, so that the acceleration
and retardation of the composite motion shall be made now in a greater
and now in a lesser ratio.
SAGR. I feel myself being gently led
by the hand; and although I find no obstacles in the road, yet like the
blind I do not see where my guide is leading me, nor have I any means
of guessing where such a journey must end.
SALV. There is a vast difference
between my slow philosophizing and your rapid insights; yet in this
particular with which we are now dealing, I do not wonder that even the
perspicacity of your mind is beclouded by the thick dark mists which
hide the goal toward which we are traveling. All astonishment ceases
when I remember how many hours, how many days, and how many more nights
I spent on these reflections; and how often, despairing of ever
understanding it, I tried to console myself by being convinced, like
the unhappy Orlando, that could not be true which had been nevertheless
brought before my very eyes by the testimony of so many trustworthy
men. So you need not be surprised if for once, contrary to custom, you
do not foresee the goal. And if you are nevertheless dismayed, then I
believe that the outcome (which so far as I know is entirely
unprecedented) will put an end to this puzzlement of yours.
SAGR. Well, thank God for not letting
your despair lead you to the end that befell the miserable Orlando, or
to that which is perhaps no less fictitiously related of Aristotle; for
then everyone, myself included, would be deprived of the revelation of
something as thoroughly hidden as it is sought after. Therefore I beg
you to satiate my greed for it as quickly as you can.
SALV. I am at your service. We have
arrived at an inquiry as to how the additions and subtractions of the
terrestrial whirling and the annual motion might be made now in greater
and now in lesser ratios; for it is such a diversity, and nothing else,
that may be assigned as a cause for the monthly and annual changes in
the size of the tides. I shall next consider three ways in which this
ratio of the additions and subtractions of the earth's rotation and the
annual motion may be made greater and less.
First, this could be done by the velocity of
the annual motion increasing and decreasing while the additions and
subtractions made by the diurnal whirling remained constant in
magnitude. For since the annual motion is about three times as fast as
the diurnal motion, even taking the latter at the equator, then if we
were to increase it further, the addition or subtraction of the diurnal
motion would make less of an alteration. On the other hand if it were
made slower, this same diurnal motion would alter it proportionately
more. Thus to add or subtract four degrees of speed when dealing with
something which moves with twenty degrees will alter its course less
than if the same four degrees were added to or subtracted from
something which moved with only ten degrees of speed.
The second way would be by making the
additions and subtractions greater or smaller, retaining the annual
motion at the same velocity. This is very easy to see, since it is
obvious that a velocity of twenty degrees (for instance) will be
altered more by the addition or subtraction of ten degrees than by the
addition or subtraction of four.
The third manner would be a combination of
these two, the annual motion diminishing and the diurnal additions and
subtractions increasing.
As you see, it was easy to get this far; yet
it was indeed a laborious task for me to discover how such effects
could be accomplished in nature. Yet I finally found something that
served me admirably. In a way it is almost unbelievable. I mean that it
is astonishing and incredible to us, but not to Nature; for she
performs with the utmost ease and simplicity things which are even
infinitely puzzling to our minds, and what is very difficult for us to
comprehend is quite easy for her to perform.
To continue, then: having demonstrated that
the proportions between the additions and subtractions of the whirling
on the one hand and the annual motion on the other may be made greater
and less in two manners (I say two, because the third is a composite of
the others), I add now that Nature does make use of both; and I add
further that if she made use of but one of them, then one of the two
periodic alterations of the tide would necessarily be removed. The
monthly periodic changes would cease if there were no variation due to
the annual motion, and if the additions and subtractions of the diurnal
rotation were kept always equal, then the annual periodic alterations
would be missing.
SAGR. Then do the monthly alterations
of the tides depend upon changes in the annual motion of the earth? And
the annual alterations in the ebb and flow are derived from the
additions and subtractions of the diurnal rotation? Now I am more
confused than ever, and farther from any hope of being able to
comprehend how this complication comes about, more intricate to my mind
than the Gordian knot. I envy Simplicio, from whose silence I deduce
that he understands everything and is free from the confusion that
beclouds my imagination. SIMP. I really believe that you are
confused, Sagredo, and I also think I know the cause of your confusion.
In my opinion this originates from your understanding a part of what
Salviati has set forth, and not understanding another part. And you are
also correct about my not being confused at all, though not for the
reason you suppose; that is, that I understand the whole thing. Quite
the contrary; I understand nothing whatever of it, and confusion lies
in the multiplicity of things -- not in nothing.
SAGR. You see, Salviati, how the
checkrein that has been applied to Simplicio in the past sessions has
gentled him, and changed him from a skittish colt into an ambling nag.
But please, without more delay, put an end
to this suspense for both of us.
SALV. I shall do my best to overcome
my obscure way of expressing myself, and the sharpness of your wits
will fill up the dark places.
There are two events whose causes we must
investigate; the first concerns the variation which occurs in the tides
over a monthly period, and the other belongs to the annual period. We
shall speak first of the monthly, and then deal with the annual; and we
must first resolve the whole according to the axioms and hypotheses
already established, without introducing any innovations either from
astronomy or from the universe to help out the tides. We shall
demonstrate that the causes for all the various events perceived in the
tides reside in things previously recognized and accepted as
unquestionably true. Thus I say that one true, natural, and even
necessary thing is that a single movable body made to rotate by a
single motive force will take a longer time to complete its circuit
along a greater circle than along a lesser circle. This is a truth
accepted by all, and in agreement with experiments, of which we may
adduce a few.
In order to regulate the time in wheel
clocks, especially large ones, the builders fit them with a certain
stick which is free to swing horizontally. At its ends they hang leaden
weights, and when the clock goes too slowly, they can render its
vibrations more frequent merely by moving these weights somewhat toward
the center of the stick. On the other hand, in order to retard the
vibrations, it suffices to draw these same weights out toward the ends,
since the oscillations are thus made more slowly and in consequence the
hour intervals are prolonged. Here the motive force is constant --the
counterpoise-- and the moving bodies are the same weights; but their
vibrations are more frequent when they are closer to the center; that
is, when they are moving along smaller circles.
Let equal weights be suspended from unequal
cords, removed from the perpendicular, and set free. We shall see the
weights on the shorter cords make their vibrations in shorter times,
being things that move in lesser circles. Again, attach such a weight
to a cord passed through a staple fastened to the ceiling, and hold the
other end of the cord in your hand. Having started the hanging weight
moving, pull the end of the cord which you have in your hand so that
the weight rises while it is making its oscillations. You will see the
frequency of its vibrations increase as it rises, since it is going
continually along smaller circles.
And here I want you to notice two details
which deserve ~ attention. One is that the vibrations of such a
pendulum are made so rigorously according to definite times, that it is
quite impossible to make them adopt other periods except by lengthening
or shortening the cord. Of this you may readily make sure by
experiment, tying a rock to a string and holding the end in your hand.
No matter how you try, you can never succeed in making it go back and
forth except in one definite time, unless you lengthen or shorten the
string; you will see that it is absolutely impossible.
The other particular is truly remarkable; it
is that the same pendulum makes its oscillations with the same
frequency, or very little different -- almost imperceptibly-- whether
these are made through large arcs or very small ones along a given
circumference. I mean that if we remove the pendulum from the
perpendicular just one, two, or three degrees, or on the other hand
seventy degrees or eighty degrees, or even up to a whole quadrant, it
will make its vibrations when it is set free with the same frequency in
either case; in the first, where it must move only through an arc of
four or six degrees, and in the second where it must pass through an
arc of one hundred sixty degrees or more. This is seen more plainly by
suspending two equal weights from two threads of equal length, and then
removing one just a small distance from the perpendicular and the other
one a very long way. Both, when set at liberty, will go back and forth
in the same times, one by small arcs and the other by very large ones.
From this follows the solution of a very
beautiful problem, which is this: Given a quarter of a circle shall
draw it here in a little diagram on the ground -- which shall be AB
here, vertical to the horizon so that it extends in the plane touching
at the point B; take an arc made of a very smooth and polished concave
hoop bending along the curvature of the circumference ADB, so that a
well-rounded and smooth ball can run freely in it (the rim of a sieve
is well suited for this experiment). Now, say that
wherever you place the ball, whether near to or far from the ultimate
limit B -- placing it at the point C, or at D, or at E-- and let it go,
it will arrive at the point B in equal times (or insensibly different),
whether it leaves from C or D or E or from any other point you like; a
truly remarkable phenomenon. Now add another, no less beautiful than
the last. This is that along all chords drawn from the point B to
points C, D, E, or any other point (taken not only in the quadrant BA,
but in the whole circumference of the entire circle), the same movable
body will descend in absolutely equal times. Thus, in the same time
which it takes to descend along the whole diameter erected
perpendicular to the point B, it will also descend along the chord BC,
even when that subtends but a single degree or yet a smaller arc.
And one more marvel: The motions of bodies
falling along the arcs of the quadrant AB are made in shorter times
than those made along the chords of the same arcs, so that the fastest
motion, made in the shortest time, by a movable body going from the
point A to the point B will be along the circumference AOB and will not
be that which is made along the straight line AB, although that is the
shortest of all the lines which can be drawn between the points A and
B. Also, take any point in that same arc (let it be, for instance, the
point O), and draw two chords AO and OB; then the moving body leaving
from the point A will get to Bin less time going along the two chords
AO and OB than going along the single chord AB. The shortest time of
all will be that of its fall along the arc AOB, and similar properties
are to be understood as holding for all lesser arcs taken upward from
the lowest limit B.
SAGR. Enough; no more; you are
confusing me so with marvels, and are distracting my mind in so many
directions, that I fear only a small part of it will remain free and
clear for me to apply to the main subject we are dealing with -- which,
I regret to say, is too obscure and difficult as it is. I beg you, as a
favor to me, that when we have finished with the theory of the tides
there shall be other days when you will again honor this house of mine
and of yours, to discuss the many other problems that have been left
dangling. Perhaps they will be no less interesting and elegant than
these which we have been treating in the days just past, and which
ought to be finished today.
SALV. I shall be at your disposal,
though we shall have to have more than one or two sessions if, in
addition to the questions reserved to be separately dealt with, we wish
to add the many that pertain both to local motion and to the motions
natural to projectiles -- subjects dealt with at length by our Lincean
Academician.
Getting back to our original purpose, we
were explaining that for things moved circularly by some motive force
which is kept continually the same, the times of circulation are
preestablished and determined, and impossible to lengthen or shorten.
Having given examples of this and brought forth sensible experiments
which we can perform, we may affirm the same to be true of our
experience of the planetary movements in the heavens, for which the
same rule is seen to hold: Those which move in the larger circles
consume the longer times in passing through them. We have the most
ready observations of this from the satellites of Jupiter, which make
their revolutions in short times. So there is no question that if, for
example, the moon, continuing to be moved by the same motive force,
were drawn little by little into smaller circles, it would acquire a
tendency to shorten the times of its periods, in agreement with that
pendulum which in the course of its vibrations had its cord shortened
by us, reducing the radius of the circumference traversed. Now this
example which I gave you concerning the moon actually takes place and
is verified in fact. Let us remember that we had already concluded with
Copernicus that it is not possible to separate the moon from the earth,
about which it unquestionably moves in a month. Let us likewise
remember that the terrestrial globe, always accompanied by the moon,
goes along the circumference of its orbit about the sun in one year, in
which time the moon revolves around the earth almost thirteen times.
From this revolution it follows that the moon is sometimes close to the
sun (that is, when it is between the sun and the earth), and sometimes
more distant (when the earth lies between the moon and the sun). It is
close, in a word, at the time of conjunction and new moon, it is
distant at full moon and opposition, and its greatest distance differs
from its closest approach by as much as the diameter of the lunar
orbit.
Now if it is true that the force which moves
the earth and the moon around the sun always retains the same strength,
and if it is true that the same moving body moved by the same force but
in unequal circles passes over similar arcs of smaller circles in
shorter times, then it must necessarily be said that the moon when at
its least distance from the sun (that is, at conjunction) passes
through greater arcs of the earth's orbit than when it is at its
greatest distance (that is, at opposition and full moon). And it is
necessary also that the earth should share in this irregularity of the
moon. For if we imagine a straight line from the center of the sun to
the center of the terrestrial globe, including also the moon's orbit,
this will be the radius of the orbit in which the earth would move
uniformly if it were alone. But if we locate there also another body
carried by the earth, putting this at one time between the earth and
the sun and at another time beyond the earth at its greatest distance
from the sun, then in this second case the common motion of both along
the circumference of the earth's orbit would, because of the greater
distance of the moon, have to be somewhat slower than in the other case
when the moon is between the earth and the sun, at its lesser distance.
So that what happens in this matter is just what happened to the rate
of the clock, the moon representing to us that weight which is attached
now farther from the center, in order to make the vibrations of the
stick less frequent, and now closer, in order to speed them up.
From this it may be clear that the annual
movement of the earth in its orbit along the ecliptic is not uniform,
and that its irregularity derives from the moon and has its periods and
restorations monthly. Now it has already been decided that the monthly
and annual periodic alterations of the tides could derive from no other
cause than from varying ratios between the annual motion and the
additions to it and subtractions from it of the diurnal rotation; and
that such alterations might be made in two ways; that is, by altering
the annual motion and keeping fixed the magnitudes of the additions, or
by changing the size of these and keeping the annual motion uniform. We
have now detected the first of these two ways, based upon the
unevenness of the annual motion; it depends upon the moon, and has its
period monthly. Thus it is necessary that for this reason the tides
should have a monthly period within which they become greater and
smaller.
Now you see how the cause of the monthly
period resides in the annual motion, and at the same time you see what
the moon has to do with this affair, and how it plays a role without
having anything to do with oceans or with waters.
SAGR. If a very high tower were shown
to someone who had no knowledge of any kind of staircase, and he were
asked whether he dared to scale such a supreme height, I believe he
would surely say no, failing to understand that it could be done in any
way except by flying. But being shown a stone no more than half a yard
high and asked whether he thought he could climb up on it, he would
answer yes, I am sure; nor would he deny that he could easily climb up
not once, but ten, twenty, or a hundred times. Hence if he were shown
the stairs by which one might just as easily arrive at the place he had
adjudged impossible to reach, I believe he would laugh at himself and
confess his lack of imagination.
You, Salviati, have guided me step by step
so gently that r I am astonished to find I have arrived with so little
effort at a height which I believed impossible to attain. It is
certainly true that the staircase was so dark that I was not aware of
my approach to or arrival at the summit, until I had come out into the
bright open air and discovered a great sea and a broad plain. And just
as climbing step by r step is no trouble, so one by one your
propositions appeared so clear to me, little or nothing new being
added, that I thought little or nothing was being gained. So much the
more is my wonder at the unexpected outcome of this argument, which has
led me to a comprehension of things I believed inexplicable.
Just one difficulty remains from which I
desire to be freed. If the movement of the earth around the zodiac in
company with the moon is irregular, such an irregularity ought to have
been observed and noticed by astronomers, but I do not know that this
has occurred. Since you are better informed on these matters than I am,
resolve this question for me and tell me what the facts are.
SALV. Your doubt is very reasonable,
and in response to the objection I say that although astronomy has made
great progress over the course of the centuries in investigating the
arrangement and movements of the heavenly bodies, it has not thereby
arrived at such a state that there are not I many things still
remaining undecided, and perhaps still more which remain unknown. It is
likely that the first observers of the sky recognized nothing but a
general motion of all the stars -- the diurnal motion-- but I think it
was not long before they discovered that the moon is inconstant about
keeping company with the other stars. Years would have passed before
they had distinguished all the planets, however. In particular, I
believe that Saturn, on account of Its slowness, and Mercury, because
of being rarely seen, were the last objects to be recognized as vagrant
and wandering. Many more years probably passed before the stoppings and
retrograde motions of the three outer planets were observed, and their
approaches and retreats from the earth, which occasioned the need to
introduce eccentrics and epicycles-- things unknown even to Aristotle,
who makes no mention of them. How long did Mercury and Venus, with
their remarkable phenomena, keep astronomers in suspended judgment
about their true locations, to mention nothing else? Thus even the
ordering of the world bodies and the integral structure of that part of
the universe recognized by us was in doubt up to the time of
Copernicus, who finally supplied the true arrangement and the true
system according to which these parts are ordered, so that we are
certain that Mercury, Venus, and the other planets revolve about the
sun and that the moon revolves around the earth. But we cannot yet
determine surely the law of revolution and the structure of the orbit
of each planet (the study ordinarily called planetary theory); witness
to this fact is Mars, which has caused modern astronomers so much
distress. Numerous theories have also been applied to the moon itself
since the time when Copernicus first greatly altered Ptolemy's theory.
Now to get down to our particular point;
that is, to the apparent motions of the sun and moon. In the former
there has been observed a certain great irregularity, as a result of
which it passes the two semicircles of the ecliptic (divided by the
equinoctial points) in very different times, consuming about nine days
more in passing over one half than the other; a difference which is, as
you see, very conspicuous. It has not yet been observed whether the sun
preserves a regular motion in passing through very small arcs, as for
example those of each sign of the zodiac, or whether it goes at a pace
now somewhat faster and now slower, as would necessarily follow if the
annual motion belongs only apparently to the sun and really to the
earth in company of the moon. Perhaps this has not even been looked
into.
As to the moon, its cycles have been
investigated principally in the interest of eclipses, for which it
suffices to have an exact knowledge of its motion around the earth. The
progress of the moon through particular arcs of the zodiac has
accordingly not been investigated in thoroughgoing detail. Therefore
the fact that there is no obvious irregularity is insufficient to cast
doubt upon the possibility that the earth and the moon are somewhat
accelerated at new moon and retarded at full moon in traveling through
the zodiac; that is, in going along the circumference of the earth's
orbit. This comes about for two reasons; first, that the effect has not
been looked for, and second, that it cannot be very large.
Nor is there any need for the irregularity
to be very large in order to produce the effect that is seen in the
alterations of the size of the tides. For not only the changes, but the
tides themselves, are small with respect to the magnitude of the bodies
in which they occur, though with respect to us and to our smallness
they seem to be great things. Adding or deducting one degree of speed
where there are naturally seven hundred or a thousand cannot be called
a large change, either in what confers it or in what receives it; and
the water of our sea, carried by the diurnal whirling, travels about
seven hundred miles per hour. This is the motion common to it and to
the earth, and therefore imperceptible to us. The motion which is made
sensible to us in currents is not even one mile per hour (I am speaking
of the open sea, and not of straits), and it is this that alters the
great, natural primary motion.
Still, such a change is considerable with
respect to us and to our ships. A vessel that can make, say, three
miles per hour in quiet water under the power of its oars, will have
its travel doubled by such a current favoring it instead of opposing
it. This is a very notable difference in the motion of the boat, though
it is quite small in the movement of the sea, which is changed by only
one seven-hundredth. I say the same of its rising and falling one, two,
or three feet-- scarcely four or five feet even at the extremity of a
basin two thousand or more miles long, where its depth is hundreds of
feet. Such a change is much less than if, in one of the barges bringing
sweet water to us, this water should rise in the prow by the thickness
of a leaf at an arrest of the barge. From this I conclude that very
small alterations with respect to the immense size and extreme speed of
the oceans would be sufficient to make great changes in them in
relation to the minuteness of ourselves and our phenomena.
SAGR. I am fully satisfied as to this
part. It remains for you to explain to us how these additions and
subtractions deriving from the diurnal whirling are increased or
diminished, upon which alterations you hinted would depend the annual
period of growth and diminution in the tides.
SALV. I shall use all my resources to
make myself understood, but the difficulty of the phenomena themselves
and the great abstractness of mind needed to understand them intimidate
me.
The irregularity of the additions and
subtractions which the diurnal rotation makes upon the annual motion
depends upon the tilting of its axis to the plane of the earth's orbit,
or ecliptic. By this tilting, the equator crosses the ecliptic and is
inclined and oblique to it with the same slope as that of the axis. The
magnitude of the additions amounts to as much as the entire diameter of
the equator when the center of the earth is at the solstitial points,
but outside of those it amounts to less and less according as the
center approaches the equinoctial points, where such additions are
least of all. This is the whole story, but it is wrapped in the
obscurity which you perceive.
SAGR. Rather in that which I do not
perceive, since so far I do not understand a thing.
SALV. That is just what I expected;
nevertheless, we shall see whether the drawing of a little diagram will
not shed some light on it. It would be better to represent this effect
by means of solid bodies than by a mere picture; however, we may get
some assistance from perspective and foreshortening. So let us show, as
before, the circumference of the earth's orbit, the point A being
supposed to be at one of the solstices and the diameter AP being the
common section of the solstitial colure and the plane of the earth's
orbit, or ecliptic. Suppose the center of the terrestrial globe to be
located at this point A; its axis, CAB, tilted to the plane of the
earth's orbit, falls in the plane of the said colure, which passes
through the axes of both equator and ecliptic. To avoid confusion, we
shall show only the equatorial circle, indicating this with the letters
DGEF, whose common section with the plane of the earth's orbit will be
the line DE, so that one half of the equator, marked DFE, will be below
the plane of the earth's orbit, and the other half, DGE, will be above
it.
It is now supposed that the revolution of the equator is in the order
of the points D, G, E, F, and that the motion of the center is toward
E. The center of the earth being at A, its axis CB (which is
perpendicular to the equatorial diameter DE) falls as we said in the
solstitial colure, the common section of this with the earth's orbit
being the diameter PA; hence this line PA will be perpendicular to DE,
because the colure is perpendicular to the earth's orbit. Therefore DE
will be tangent to the earth's orbit at the point A, so that in this
position the motion of the center along the arc AE, which amounts to
one degree per day, would vary but little; it would even be as if it
were along the tangent DAE. And since the diurnal rotation, carrying
the point D through G to E, is increased over the motion of the center
(which moves practically along this same line DE) by as much as the
whole diameter DE, while on the other hand the other semicircle EFD is
diminished by the same amount in its motion, the additions and
subtractions at this point (that is, at the time of the solstice) will
be measured by the entire diameter DE.
Next we shall see whether they are of the
same magnitude at the times of the equinoxes. Transporting the center
of the earth to the point I, one quadrant away from the point A, let us
take the same equator GEFD, its common section DE with the ecliptic,
and its axis CB at the same tilt. Now the tangent to the ecliptic at
the point I will no longer be DE, but a different one, cutting this at
right angles. This will be marked HIL, in the direction of which will
be the motion of the center I, proceeding along the circumference of
the earth's orbit. Now in this situation the additions and subtractions
are not measured anymore by the diameter DE, as they were at first,
f9rsince this diameter does not extend along the line of the annual
motion HL, but rather cuts it at right angles, D and E add and subtract
nothing.
The additions and subtractions must now be
taken along that diameter which falls in the plane perpendicular to
that of the earth's orbit and cutting it in the line HL let this be the
diameter GF. The additive motion will then be made by the point G along
the semicircle GEF, and the subtractive motion will be the balance,
along the other semicircle FDG. Now this diameter being not in the same
line as the annual motion, HL, but cutting it as is seen in the point I
(with the point G being elevated above and F depressed below the plane
of the earth's orbit), the additions and subtractions are not
determined by its entire length. Rather, they must be that fraction of
it taken between the parts of the line HL which are cut off between the
perpendiculars drawn upon it from the points G and F, which would be
two lines GS and FV: Hence the measure of the additions is the line SV,
and this is less than GF or DE, which was the measure of the additions
at the solstice A.
According, then, to the placement of the
center of the earth at any other point of the quadrant AI, we draw the
tangent at such a point and drop perpendiculars upon it from the ends
of the equatorial diameter determined by the plane through this tangent
vertical to the plane of the ecliptic; and such apart of this tangent,
which will be always less toward the equinoxes and greater toward the
solstices, will give us the magnitudes of the additions and
subtractions. Then as to how much the least additions differ from the
greatest, this is easy to determine; between these there is the same
variation as between the whole axis (or diameter) of the globe and that
part of it which lies between the polar circles. This is less than the
whole diameter by one-twelfth, approximately, assuming that the
additions and subtractions are made at the equator; in other latitudes
they are less in proportion as their diameters are diminished.
That is all I can tell you about the matter,
and perhaps it is as much as can be comprehended within our knowledge--
which, as is well known, can be only of such conclusions as are fixed
and constant. Such are the three general periods of the tides, since
these depend upon invariable causes which are unified and eternal. But
with these primary and universal causes there are mixed others which,
though secondary and particular, are capable of making great
alterations; and these secondary causes are partly variable and not
subject to observations (the changes due to winds, for example), and
partly, though determinate and fixed, are not observed because of their
complication. Such are the lengths of the sea basins, their various
orientations in one direction or another, and the many and various
depths of the waters. Who could possibly formulate a complete account
of these except perhaps after very lengthy observations and reliable
reports? Without this, what could serve as a sound basis for hypotheses
and assumptions on the part of anyone who, from such a combination,
wished to furnish adequate reasons for all the phenomena? And, I might
add, for the anomalies and particular irregularities that can be
perceived in the movements of the waters?
I am content to have noticed that incidental
causes do exist in nature, and that they are capable of producing many
alterations; I shall leave their minute observation to those who
frequent the various oceans. I merely call to your attention, in
bringing this conversation of ours to a close, that the precise
durations of the ebbing and flowing are changed not only by the lengths
and depths of the basins, but I believe that noteworthy variations are
also introduced by the juncture of various stretches of ocean which
differ in size and in situation or, let us say, in orientation. Such a
contrast occurs right here in the Adriatic Gulf, which is much smaller
than the rest of the Mediterranean and is placed at such a different
orientation that whereas the latter has its closed end in the eastern
part at the shores of Syria, the former is closed at its western part.
And since it is at the extremities that by far the greatest tides
occur-- indeed, nowhere else are there very great risings and
fallings-- it may very well be that the times of flood at Venice occur
during the ebbings of the other sea. The Mediterranean, being much
larger and extending more directly from west to east, in a certain
sense dominates the Adriatic. Hence it would not be surprising if the
effects that depend upon the primary causes were not verified in the
Adriatic at the appointed times and corresponding to the proper
periods, as well at least as they would be in the rest of the
Mediterranean. But this matter would require long observations which I
have not made in the past, nor shall I be able to make them in the
future.
SAGR. It seems to me that you have
done a great deal by opening the first portal to such lofty
speculations. In your first general proposition, which seems to me to
admit of no refutation, you have explained very persuasively why it
would be impossible for the observed movements to take place in the
ordinary course of nature if the basins containing the waters of the
seas were standing still, and that on the other hand such alterations
of the seas would necessarily follow if one assumed the movements
attributed by Copernicus to the terrestrial globe for quite other
reasons. If you had given us no more, this alone seems to me to excel
by such a large margin the trivialities which others have put forth
that just to think of those once more makes me ill. And I am much
astonished that among men of sublime intellect, of whom there have been
plenty, none have been struck by the incompatibility between the
reciprocating motion of the contained waters and the immobility of the
containing vessels, a contradiction which now seems so obvious to me.
SALV. What is more to be wondered at,
once it had occurred to the minds of some to refer the cause of the
tides to the motion of the earth (which showed unusual perspicacity on
the part of these men), is that in seizing at this matter they should
have caught onto nothing. But this was because they did not notice that
a simple and uniform motion, such as the simple diurnal motion of the
terrestrial globe for instance, does not suffice, and that an uneven
motion is required, now accelerated and now retarded. For if the motion
of the vessels were uniform, the contained waters would become
habituated to it and would never make any mutations.
Likewise it is completely idle to say (as is
attributed to one of the ancient mathematicians) that the tides are
caused by the conflict arising between the motion of the earth and the
motion of the lunar sphere, not only because it is neither obvious nor
has it been explained how this must follow, but because its glaring
falsity is revealed by the rotation of the earth being not contrary to
the motion of the moon, but in the same direction. Thus everything that
has been previously conjectured by others seems to me completely
invalid. But among all the great men who have philosophized about this
remarkable effect, I am more astonished at Kepler than at any other.
Despite his open and acute mind, and though he has at his fingertips
the motions attributed to the earth, he has nevertheless lent his ear
and his assent to the moon's dominion over the waters, to occult
properties, and to such puerilities.
SAGR. It is my guess that what has
happened to these more reflective men is what is happening at present
to me; namely, inability to understand the interrelation of the three
periods, annual, monthly, and diurnal, and how their causes may seem to
depend upon the sun and the moon without either of these having
anything to do with the water itself. This matter, for a full
understanding of which I need a longer and more concentrated
application of my mind, is still obscure to me because of its novelty
and its difficulty. But I do not despair of mastering it by going back
over it by myself, in solitude and silence, and ruminating on what
remains undigested in my mind.
In the conversations of these four days we
have, then, strong evidences in favor of the Copernican system, among
which three have been shown to be very convincing-- those taken from
the stoppings and retrograde motions of the planets, and their
approaches toward and recessions from the earth; second, from the
revolution of the sun upon itself, and from what is to be observed in
the sunspots; and third, from the ebbing and flowing of the ocean
tides.
SALV. To these there may perhaps be
added a fourth, and maybe even a fifth. The fourth, I mean, may come
from the fixed stars, since by extremely accurate observations of these
there may be discovered those minimal changes that Copernicus took to
be imperceptible. And at present there is transpiring a fifth novelty
from which the mobility of the earth might be argued. This is being
revealed most perspicuously by the illustrious Caesar Marsili, of a
most noble family at Bologna, and a Lincean Academician. He explains in
a very learned manuscript that he has observed a continual change,
though a very slow one, in the meridian line. I have recently seen this
treatise, and it has much astonished me. I hope that he will make it
available to all students of the marvels of nature.
SAGR. This is not the first time that
I have heard mention of the subtle learning of this gentleman, who has
shown himself to be the zealous protector of all men of science and
letters. If this or any other of his works is made public, we may be
sure in advance that it will become famous.
SALV. Now, since it is time to put an
end to our discourses, it remains for me to beg you that if later, in
going over the things that I have brought out, you should meet with any
difficulty or any question not completely resolved, you will excuse my
deficiency because of the novelty of the concept and the limitations of
my abilities; then because of the magnitude of the subject; and finally
because I do not claim and have not claimed from others that assent
which I myself do not give to this invention, which may very easily
turn out to be a most foolish hallucination and a majestic paradox.
To you, Sagredo, though during my arguments
you have shown yourself satisfied with some of my ideas and have
approved them highly, I say that I take this to have arisen partly from
their novelty rather than from their certainty, and even more from your
courteous wish to afford me by your assent that pleasure which one
naturally feels at the approbation and praise of what is one's own. And
as f you have obligated me to you by your urbanity, so Simplicio has
pleased me by his ingenuity. Indeed, I have become very fond of him for
his constancy in sustaining so forcibly and so undauntedly the
doctrines of his master. And I thank you, Sagredo, for your most
courteous motivation, just as I ask pardon of Simplicio if I have
offended him sometimes with my too heated and opinionated speech. Be
sure that in this I have not been moved by any ulterior purpose, but
only by that of giving you every opportunity to introduce lofty
thoughts, that I might be the better informed.
SIMP. You need not make any excuses;
they are superfluous, and especially so to me, who, being accustomed to
public debates, have heard disputants countless times not merely grow
angry and get excited at each other, but even break out into insulting
speech and sometimes come very close to blows.
As to the discourses we have held, and
especially this last one concerning the reasons for the ebbing and
flowing of the ocean, I am really not entirely convinced; but from such
feeble ideas of the matter as I have formed, I admit that your thoughts
seem to me more ingenious than many others I have heard. I do not
therefore consider them true and conclusive; indeed, keeping always
before my mind's eye a most solid doctrine that I once heard from a
most eminent and learned person, and before which one must fall silent,
I know that if asked whether God in His infinite power and wisdom could
have conferred upon the watery element its observed reciprocating
motion using some other means than moving its containing vessels, both
of you would reply that He could have, and that He would have known how
to do this in many ways which are unthinkable to our minds. From this I
forthwith conclude that, this being so, it would be excessive boldness
for anyone to limit and restrict the Divine power and wisdom to some
particular fancy of his own.
SALV. An admirable and angelic
doctrine, and well in accord with another one, also Divine, which,
while it grants to us the right to argue about the constitution of the
universe (perhaps in order that the working of the human mind shall not
be curtailed or made lazy) adds that we cannot discover the work of His
hands. Let us, then, exercise these activities permitted to us and
ordained by God, that we may recognize and thereby so much the more
admire His greatness, however much less fit we may find ourselves to
penetrate the profound depths of His infinite wisdom.
SAGR. And let this be the final
conclusion of our four days' arguments, after which if Salviati should
desire to take some interval of rest, our continuing curiosity must
grant that much to him. But this is on condition that when it is more
convenient for him, he will remain and satisfy our desires-- mine in
particular-- regarding the problems set aside and noted down by me to
submit to him at one or two further sessions, in accordance with our
agreement. Above all, I shall be waiting impatiently to hear the
elements of our Academician's new science of natural and constrained
local motions.
Meanwhile, according to our custom, let us
go and enjoy an hour of refreshment in the gondola that awaits us.
END OF THE
FOURTH AND FINAL DAY
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