First, around the center A, I describe the circumference of the annual orbit BC; on it let us take any point whatever B, and using B as a center let us describe this smaller circle DEFG, representing the terrestrial globe; then let us assume the center B to run along the whole circumference of the annual orbit from west to east, namely, from B toward C; and let us further assume the terrestrial globe to turn around its own center B in the period of twenty-four hours, also from west to east, namely, according to the order of the points D, E, F, and G. Here we must note carefully that as a circle turns around its own center, each part of it must move in opposite directions at different times; this is clear by considering that, while the parts of the circumference around the point D move toward the left (namely, toward E), those on the opposite side (which are around F) advance toward the [453] right (namely, toward G), so that when the parts D are at F their motion is contrary to what it was when they were at D; furthermore, at the same time that the parts E descend (so to speak) toward F, the parts G ascend toward D. Given such a contrariety in the motions of the parts of the terrestrial surface as it turns around its own center, it is necessary that in combining this diurnal motion with the other annual one there results an absolute motion of the parts of the terrestrial surface that is sometimes highly accelerated and sometimes retarded by the same amount. This is clear from the following considerations: the absolute motion of the part around D is very fast since it originates from two motions in the same direction, namely, toward the left; the first of these is the annual motion common to all parts of the globe, the other is the motion of point D carried also toward the left by the diurnal rotation; hence, in this case the diurnal motion increases and accelerates the annual motion; the opposite of this happens at the opposite side F, which is carried toward the right by the diurnal rotation while together with the whole globe it is carried toward the left by the common annual motion; thus, the diurnal motion takes away from the annual, and so the absolute motion resulting from the combination of the two turns out to be greatly retarded; finally, around the points E and G the absolute motion remains equal to the annual alone, for the diurnal motion adds or subtracts little or nothing, its direction being neither left nor right but down and up. Therefore, we conclude that, just as it is true that the motion of the whole globe and of each of its parts would be invariable and uniform if it were moving with a single motion (be it the simple annual or the diurnal alone), so it is necessary that the mixture of these two motions together gives the parts of the globe variable motions (sometimes accelerated and sometimes retarded) by means of additions or subtractions of the diurnal rotation and the annual revolution. Thus, if it is true (and it is most true, as experience shows) that the acceleration and retardation of a vessel’s motion make the water contained in it run back and forth along its length and rise and fall at its ends, who will want to raise difficulties about granting that such an effect can (or rather, must necessarily) happen in seawater, which is contained in various basins subject to similar variations, especially in those whose length stretches out from west to east (which is the direction along which these basins move)?
[454] Now, let this be the primary and most important cause of the tides, without which this effect would not happen at all. However, there are many different particular phenomena which can be observed in different places and at different times, and which must depend on other different concomitant causes, although these must all be connected with the primary cause; hence, it is proper to present and examine the various factors that may be the causes of such various phenomena.
The first of these is that whenever water is made to flow toward one or the other end of a containing vessel by a noticeable retardation or acceleration of that vessel, and it rises at one end and subsides at the other, it does not thereby remain in such a state even if the primary cause should cease; instead, in virtue of its own weight and natural inclination to level and balance itself out, it spontaneously and quickly goes back; and, being heavy and fluid, not only does it move toward equilibrium, but carried by its own impetus, it goes beyond and rises at the end where earlier it was lower; not resting here either, it again goes back, and with more repeated oscillations, it indicates that it does not want to change suddenly from the acquired speed to the absence of motion and state of rest, but that it wants to do it gradually and slowly. This is similar to the way in which a pendulum, after being displaced from its state of rest (namely, from the perpendicular), spontaneously returns to it and to rest, but not before having gone beyond it many times with a back-and-forth motion.
The second factor to notice is that the reciprocal motions just mentioned take place and are repeated with greater or lesser frequency, namely, in shorter or longer times, depending on the length of the vessels containing the water; thus, the oscillations are more frequent for the shorter distances and rarer for the longer. And this is exactly what happens in the same example of pendulums, where we see that the oscillations of those hanging from a longer string are less frequent than those of pendulums hanging from shorter strings.
And here is a third important point to know: it is not only the greater or lesser length of the vessel that causes the water to make its oscillations in different times, but the greater or lesser depth brings about the same thing; what happens is that, for water contained [455] in vessels of equal length but of unequal depth, the one which is deeper makes its oscillations in shorter times, and the vibrations of less deep water are less frequent.69
Fourth, worthy of notice and of diligent observation are two effects produced by water in such vibrations. One is the alternating rising and falling at both ends; the other is the flowing back and forth, horizontally, so to speak. These two different motions affect different parts of the water differently. For its ends are the parts that rise and fall the most; those at the middle do not move up or down at all; and as for the rest, those that are nearer the ends rise and fall proportionately more than the farther parts. On the contrary, in regard to the lateral motion back and forth, the middle parts go forth and come back a great deal; the water at the ends does not flow at all except insofar as by rising it goes over the embankment and overflows its original bed, but where the embankment stands in the way and can hold it, it only rises and falls; finally, the water in the middle is not the only part that flows back and forth, for this is also done proportionately by its other parts, as they flow more or less depending on how far or near they are relative to the middle.
The fifth particular factor must be considered much more carefully, insofar as it is impossible for us to reproduce it experimentally and practically.70 The point is this. In artificial vessels which, like the boats mentioned above, move now more and now less swiftly, the acceleration or retardation is shared to the same extent by the whole vessel and all its parts: thus, for example, as the boat slows down, the forward part is not retarded any more than the back, but they all share the same retardation equally; the same happens in acceleration; that is, as the boat acquires greater speed, both the bow and the stern are accelerated in the same way. However, in very large vessels like the very long basins of the seas, though they are nothing but certain hollows carved out of the solid terrestrial globe, nevertheless amazingly their extremities do not increase or diminish their motion together, equally, and simultaneously; [456] instead it happens that, when one extremity is greatly retarded in virtue of the combination of the diurnal and annual motions, the other extremity finds itself still experiencing very fast motion.
For easier comprehension, let us explain this by referring to the diagram drawn here. In it, let us consider, for example, a portion of water spanning a quarter of the globe, such as the arc BC; here, as we explained above, the parts at B are in very fast motion due to the combination of the diurnal and annual motions in the same direction, whereas the parts at C are retarded insofar as they lack the forward motion deriving from the diurnal rotation. If, then, we take a sea basin whose length equals the arc BC, we see how its extremities mov
e simultaneously with great inequality. The differences would be greatest for the speeds of an ocean a hemisphere long and situated in the position of the arc BCD, for the end B would be in very fast motion, the other D would be in very slow motion, and the middle parts at C would have an intermediate speed; further, the shorter a given sea is, the less will it experience this curious effect of having its parts moving at different speeds during certain hours of the day. Thus, if, as in the first case, we observe acceleration and retardation causing the contained water to flow back and forth despite the fact that they are shared equally by all parts of the vessel, what shall we think must happen in a vessel placed so curiously that its parts acquire retardation and acceleration very unequally? It seems certain we can say only that here we have a greater and more amazing cause of even stranger movements in the water. Though many will consider it impossible that we could experiment with the effects of such an arrangement by means of machines and artificial vessels, nevertheless it is not entirely impossible; I have under construction a machine in which one can observe in detail the effect of these amazing combinations of motions. However, regarding the present subject, let us be satisfied with what you may have been able to understand with your imagination so far.
[457] SAGR. For my part, I understand very well how this marvelous phenomenon must necessarily take place in the sea basins, especially in those that extend for long distances from west to east, namely, along the course of the motions of the terrestrial globe; moreover, just as it is in a way inconceivable and unparalleled among the motions we can reproduce, so I have no difficulty believing that it may produce effects which cannot be duplicated with our artificial experiments.
SALV. After these things have been clarified, it is time for us to go on and examine the variety of particular phenomena which experience enables us to observe in regard to the tides. First, there will be no difficulty understanding why it happens that there are no noticeable tides in ponds, lakes, and even small seas; this has two very effective causes.
One is that, as the basin acquires different degrees of speed at different hours of the day, because of its smallness they are acquired with little difference by all its parts, and the forward as well as the backward parts (namely, the eastern and the western) are accelerated and retarded almost in the same way; moreover, since this change occurs gradually, and not by a sudden obstacle and retardation or an immediate and large acceleration in the motion of the containing basin, it as well as all its parts receive equally and slowly the same degrees of speed; from this uniformity it follows that the contained water too receives the same action with little resistance, and consequently it gives very little sign of rising and falling and of flowing toward this or the other end. This effect is also clearly seen in small artificial containers, in which the water acquires the same degrees of speed whenever the acceleration or the retardation takes place in a relatively slow and uniform manner. However, in sea basins that extend for a great distance from east to west the acceleration or retardation is much more noticeable and unequal, for while one end is undergoing very retarded motion the other is still moving very rapidly.
The other cause is the reciprocal vibration of the water stemming from the impetus it also receives from the container, which vibration has very frequent oscillations in small vessels, as we have seen: for [458] the earth’s motions can cause agitation in the waters only at twelve-hour intervals, since the motion of the containing basins is retarded and is accelerated the maximum amount only once a day, respectively; but the second cause depends on the weight of the water while in the process of reaching equilibrium, and it has its oscillations at intervals of one hour, or two, or three, etc., depending on the length of the basin; now, mixed with the former cause, which is very small in small vessels, the latter renders it completely imperceptible; for before the end of the operation of the primary cause with the twelve-hour period, the secondary one due to the weight of the water comes about, and with its period of one hour, two, three, or four, etc. (depending on the size and depth of the basin), it perturbs and removes the first, without allowing it to reach the maximum or the middle of its effect. From this contraposition, any sign of tides remains completely annihilated or much obscured.
I say nothing of the constant alterations due to air; disturbing the water, they would not allow us to ascertain a very small rise or fall of half an inch or less, which might actually be taking place in water basins that are no longer than a degree71 or two.
Second, I come to resolving the difficulty of how tidal periods can commonly appear to be six hours, even though the primary cause embodies a principle for moving the water only at twelve-hour intervals, that is, once for the maximum speed of motion and once for maximum slowness. To this I answer that such a determination cannot in any way result from the primary cause alone; instead we must add the secondary ones, namely, the greater or lesser length of the vessels and the greater or lesser depth of the water contained in them. Although these causes do not act to bring about the motions of the water (since this action originates only from the primary cause), nevertheless they have a key role in determining the periods of the oscillations, and this role is so powerful that the primary cause remains subject to them. Thus, the six-hour interval is no more proper or natural than other time intervals, although it is perhaps the one most commonly observed since it occurs in our Mediterranean, which for many centuries was the only accessible sea; however, such a period is not [459] observed in all its regions, for in some of the more narrow areas such as the Hellespont and the Aegean, the periods are much shorter and also much different from each other. Some say that Aristotle long observed these variations from some cliffs in Euboea and found their causes incomprehensible, and that because of this, (overcome with despair) he jumped into the sea and drowned himself.72
Third, we can quickly explain why it happens that although some seas are very long—for example, the Red Sea—nevertheless they are almost entirely lacking in tides. This occurs because its length does not extend from east to west, but from southeast to northwest. For, the earth’s motions being from west to east, the impulses received by the water always cross the meridians and do not move from one parallel to another; so, in seas that extend transversely in the direction of the poles and that are narrow in the other direction, no cause of tides remains but the contribution of some other sea with which they are connected and which is subject to large motions.
Fourth, we can very easily understand the reason why, in regard to the rise and fall of the water, tides are greatest at the extremities of gulfs and smallest in the middle. This is shown by daily experience here in Venice, which is located at the end of the Adriatic and where this variation amounts to five or six feet; but in areas of the Mediterranean far from the extremities, such a variation is very small, as is the case in the islands of Corsica and Sardinia and on the shores of Rome and Leghorn, where it does not exceed half a foot. We can also understand how, on the contrary, in places where the rise and the fall are very small, the flow back and forth is large. I say it is easy to understand the cause of these phenomena because we can make clear tests in all sorts of vessels we can artificially build; here the same effects are seen to follow naturally from our making them move with a motion which is nonuniform, namely, sometimes accelerated and sometimes retarded.
Fifth, considering how the same quantity of water that moves slowly through a wide area must flow with great impetus when passing through a narrow place, we shall have no difficulty in understanding the cause of the immense currents which flow in the narrow channel that separates Calabria from [460] Sicily; for although all the water contained in the eastern Mediterranean and bound by the width of the island and the Ionian Gulf may slowly flow into it toward the west, nevertheless, when constricted into this strait between Scylla and Charybdis,73 it flows rapidly and undergoes very great agitation. Similar to this and much greater we understand are the currents between Africa and the large island of Madagascar, as the waters of the North
and South Indian Ocean, which surround it, flow and become constricted in the smaller channel between it and the South African coast. Very great must be the currents in the Strait of Magellan, which connects the extremely vast South Atlantic and South Pacific Oceans.
Sixth, to account for some more obscure and implausible phenomena observed in this subject, we now have to make another important consideration about the two principal causes of tides and then mix them together. The first and simpler of these is (as we have said several times) the definite acceleration and retardation of the earth’s parts, from which the water would acquire a definite tendency to flow toward the east and to go back toward the west within a period of twenty-four hours. The other is the one that depends on the mere weight of water: once stirred by the primary cause, it then tries to reach equilibrium by repeated oscillations; these are not determined by a single period in advance, but they have as many temporal differences as the different lengths and depths of sea basins; and insofar as they depend on this second principle, some oscillations might flow back and forth in one hour, others in two, four, six, eight, ten, etc. Now, let us begin to join together the primary cause, whose fixed period is twelve hours, with one of the secondary causes whose period is, for example, five hours: sometimes it will happen that the primary and secondary causes agree by both producing impulses in the same direction, and with such a combination (a unanimous consent, so to speak) the tides are large; other times, the primary impulse being somehow opposite to that of the secondary cause, and thus one principle taking away what the other one gives, the watery motions will weaken and the sea will reduce to a very calm and almost motionless state; finally, [461] on still other occasions, when the same two causes neither oppose nor reinforce each other, there will be other variations in the increase or decrease of the tides. It may also happen that of two very large seas connected by a narrow channel, due to the mixture of the two causes of motion, one sea has tidal motions in one direction while the other has them in the opposite; in this case, in the channel where the two seas meet there are extraordinary agitations with contrary motions, vortices, and very dangerous boilings, as it is in fact constantly observed and reported. These conflicting motions, dependent on the different positions and lengths of interconnected seas and on their different depths, give rise sometimes to those irregular disturbances of the water whose causes have worried and continue to worry sailors, who experience them without seeing winds or any other serious atmospheric disturbance that might produce them.
The Essential Galileo Page 33