The Essential Galileo (44 page)

[452] S
IMP.
    To me, who am neither a mathematician nor an astronomer, this seems at first sight like a great paradox; if it is true that while the motion of the whole is regular, the motion of the parts that remain always attached to the whole can be irregular, then the paradox will destroy the axiom affirming that the reasoning applying to the whole and to the parts is the same.

S
ALV.
    I will demonstrate my paradox and will leave to you, Simplicio, the task of defending the axiom from it or making them consistent; my demonstration will be short and very easy and will depend on the things discussed at length in our past arguments, when we did not introduce so much as a word about the tides.

We said that there are two motions attributed to the terrestrial globe: the first is the annual motion performed by its center along the circumference of the annual orbit in the plane of the ecliptic and in the order of the signs of the zodiac, namely, from west to east; the other is performed by the same globe rotating around its own center in twenty-four hours, likewise from west to east, but around an axis somewhat inclined and not parallel to that of the annual revolution. From the combination of these two motions, each of which is in itself uniform, there results, I say, a variable motion for the parts of the earth; I will explain this by drawing a diagram, so that it can be more easily understood.

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 move 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] S
AGR.
    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.