The Essential Galileo (39 page)

S
ALV.
    On the contrary, I wish you to continue believing firmly that the result on the earth should correspond to the one on the ship, as long as you do not feel like changing your mind if this were discovered to be prejudicial to your cause.

You say: because when the ship [170] stands still the rock falls at the foot of the mast, and when the ship is in motion it falls away from the foot, therefore, inverting, from the rock falling at the foot one infers the ship to be standing still, and from its falling away one argues for the ship being in motion; but what happens to the ship must likewise happen to the terrestrial globe; hence, from the rock falling at the foot of the tower, one necessarily infers the immobility of the terrestrial globe. Is this not your reasoning?

S
IMP.
    Exactly. You have made it concise and very easy to understand.

S
ALV.
    Now, tell me, if the rock released from the top of the mast were to strike the same spot on the ship when it is going forward at great speed as when it is standing still, what use would these experiments have for ascertaining whether the vessel is standing still or going forward?

S
IMP.
    Absolutely none. Similarly, for example, from a pulse beat we cannot learn whether someone is asleep or awake since the pulse beats in the same manner in people who are asleep and who are awake.

S
ALV.
    Very well. Now, have you ever made the ship experiment?

S
IMP.
    I have never made it, but I really believe that those authors who put it forth have diligently made the observations. Furthermore, the cause of the disparity is so well known that there is no room for doubt.

S
ALV.
    It is possible that those authors put it forth without having made it; you are a good witness to this yourself, for without having made it you present it as certain and in good faith rely on their assertion. At any rate, it is not only possible but necessary that they too relied on their predecessors, without ever arriving at someone who made it; for whoever performs the experiment will find it to show the complete opposite of what is written; that is, it will show that the rock always falls at the same spot on the ship, whether it is standing still or moving at any speed. Hence, since the same holds for the earth as for the ship, from the rock falling always perpendicularly to the foot of the tower nothing can be inferred about the earth's motion or rest.

S
IMP.
    If you were referring me to some means other than experiment, I really think our disagreements would not end very soon; for this seems to me an issue so remote from any human speculation that it leaves no room for considerations of credibility or probability.

[171] S
ALV.
    And yet I think it does.

S
IMP.
    So, you did not make one hundred tests, or even one, and yet you claim the result to be certain and unequivocal? I am skeptical about this, and I go back to my certainty that the experiment has been made by the principal authors who use it, and that it shows what they claim.

S
ALV.
    Without experiment I am certain the result will happen as I say because it is necessary that it should happen that way; I add that even you yourself know that it cannot happen otherwise, although you pretend (or try to pretend) not to know it. However, I am so good at picking people's brains that I will make you admit it by force. Sagredo is very quiet, but I thought I saw him gesturing to say something.

S
AGR.
    Truly I wanted to say something or other. But then I heard you threaten Simplicio with violence, to make him reveal the knowledge he wants to conceal from us; this made me so curious that I put away any other desire. So I beg you to make good your boast.

S
ALV.
    As long as Simplicio is willing to answer my questions, I will not fail.

S
IMP.
    I will answer what I know and am certain I will have little difficulty; for knowledge is about truths and not about falsehoods, and thus I do not think I know anything about the things I regard as false.

S
ALV.
    I do not want you to say or answer anything but what you are sure you know. So, tell me, suppose you had a plane surface very polished like a mirror and made of a hard material like steel; suppose it was not parallel to the horizon but somewhat inclined; and suppose that on it you placed a perfectly spherical ball made of a heavy and very hard material like bronze, for example; what do you think it would do when released? Do you not think (as I believe) that it would stand still?

S
IMP.
    If that surface were inclined?

S
ALV.
    Yes, for this is the supposition.

S
IMP.
    I do not think it would stand still; rather I am sure it would spontaneously move downward along the incline.

S
ALV.
    Be very careful about what you say, Simplicio; for I am sure it would stand still in any spot you had placed it.

S
IMP.
    Salviati, when you make this sort of [172] assumption, I begin to be less surprised that you should arrive at very false conclusions.

S
ALV.
    Are you thus very sure that it would spontaneously move downwards along the incline?

S
IMP.
    What is there to doubt?

S
ALV.
    And you firmly believe this not because I taught it to you (for I tried to persuade you of the opposite), but because you arrived at it on your own using your natural judgment.

S
IMP.
    Now I understand your trick; you said what you did in order to lead me on and (as the popular expression goes) to trap me, not because you really believed that.

S
ALV.
    That is correct. Now, how long would the ball's motion last, and what speed would it have? Notice that I am referring to a perfectly round ball and a fastidiously polished plane, in order to remove all external and accidental impediments; similarly, I want you to disregard the impediment offered by the air through its resistance to being parted, and any other accidental obstacles there may be.

S
IMP.
    I understand everything very well. As for your question, I answer that the ball would continue to move ad infinitum, as far as the inclination of the plane extends; that it would move with continuously accelerated motion, for such is the nature of falling bodies, which “acquire strength as they keep going”;
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and that the greater the inclination, the greater would be the speed.

S
ALV.
    However, if someone wanted to have the ball move upward along the same surface, do you think it would move that way?

S
IMP.
    Not spontaneously; but it would if dragged along or thrown by force.

S
ALV.
    So, if it were propelled by some impetus forcibly impressed on it, what would its motion be and how long would it last?

S
IMP.
    Its motion would keep on being continuously reduced and retarded, due to its being against nature; and it would last more or less depending on the greater or smaller impulse and on the steeper or gentler inclination.

S
ALV.
    Therefore, I think that up to now you have explained to me the following properties of a body moving along a plane in two different directions: when descending on an inclined plane, the heavy body is spontaneously and continuously accelerated, and it requires the use of force to keep it at rest; on the other hand, in an [173] ascending path a force is needed to make it move that way (as well as to keep it at rest), and the motion impressed on it is continuously diminishing, so that eventually it is annihilated. You also say that in both cases there is a difference stemming from the greater or smaller inclination of the plane; so that a greater inclination leads to a greater downward speed, but on an upward path the same body thrust by the same force moves a greater distance when the inclination is less. Now tell me what would happen to the same body on a surface that is not inclined.

S
IMP.
    Here I must think a little before I answer. Since there is no downward slope, there cannot be a natural tendency to move; since there is no upward slope, there cannot be a resistance to being moved; thus, the body would be indifferent to motion, and have neither a propensity nor a resistance to it; I think, therefore, that it should remain there naturally at rest. Sorry to have forgotten, for I now remember that not long ago Sagredo explained to me that this is what would happen.

S
ALV.
    I think so, if one were to place it there motionless; but if it were given an impetus in some direction, what would happen?

S
IMP.
    It would move in that direction.

S
ALV.
    But with what sort of motion? A continuously accelerated one, as on a downward slope, or a progressively retarded one, as on an upward slope?

S
IMP.
    I see no cause for acceleration or retardation since there is neither descent nor ascent.

S
ALV.
    Yes. But if there is no cause for retardation, still less is there cause for rest. So, how long do you think the moving body would remain in motion?

S
IMP.
    As long as the extension of that surface which is sloping neither upward nor downward.

S
ALV.
    Therefore, if such a surface were endless, the motion on it would likewise be endless, namely, perpetual?

S
IMP.
    I think so, as long as the moving body was made of durable material.

S
ALV.
    This has already been supposed, for we have already said that all accidental and external impediments should be removed, and in this regard the body's fragility is one of the accidental impediments.
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Now tell me, what do you think is the reason why that ball moves spontaneously on the downward path and not without force on the upward one?

[174] S
IMP.
    Because the tendency of heavy bodies is to move toward the center of the earth, and only by force do they move upward away from it; and by moving down on an inclined surface one gets closer to the center, and by moving up one gets further away.

S
ALV.
    Therefore, a surface sloping neither downward nor upward would have to be equidistant from the center at all of its points. But are there any such surfaces in the world?

S
IMP.
    There is no lack of them: one is the surface of our terrestrial globe, if it were smoothed out, and not rough and mountainous, as it is; another is the surface of the water when it is calm and tranquil.

S
ALV.
    Therefore, a ship moving in a calm sea is a body going over a surface that slopes neither downward nor upward, and so it has the tendency to move endlessly and uniformly with the impulse once acquired if all accidental and external obstacles are removed.

S
IMP.
    It seems that it must be so.

S
ALV.
    Now, when the rock at the top of the mast is being carried by the ship, does it not also move along the circumference of a circle around the center, and consequently with a motion indelibly inherent in it as long as external impediments are removed? And is this motion not as fast as that of the ship?

S
IMP.
    So far, so good; but what about the rest?

S
ALV.
    You should be able to draw the last consequence yourself, if on your own you have discovered all the premises.

S
IMP.
    By the last conclusion you mean that, since the rock is moving with a motion indelibly impressed on it, it will not leave but follow the ship, and at the end it will fall at the same spot where it falls when the ship stands still; and I, too, say that this would follow if there were no external impediments to disturb the rock's motion after being released. However, there are two such impediments: one is that the moving body is incapable of parting the air merely by means of its impetus, once it loses that of the oars' power, which it shared when it was part of the ship while still at the top of the mast; the other is the newly acquired motion of falling down, which must be an impediment to its horizontal motion.

S
ALV.
    Regarding the impediment of the air, I do not deny it; and if the falling body were made of a light material like a feather or a lock [175] of wool, the retardation would be very great; but for a heavy rock it is very little. A short while ago you said yourself that the force of the strongest wind does not suffice to displace a big rock; now, think what will happen when the calm air meets the rock moving no faster than the ship as a whole. However, as I said, I grant you the small effect which may result from this impediment, just as I know you will grant me that if the air were moving at the same speed as the ship and the rock, the impediment would be absolutely nil.

Regarding the impediment of the newly acquired downward motion, first it is clear that these two motions (namely, the circular around the center and the straight toward the center) are neither contrary nor incompatible nor destructive of each other; for the moving body has no repugnance toward such motion; you yourself already granted that its repugnance is to motion which takes it farther from the center, and that its inclination is to motion which brings it closer to the center; so it follows necessarily that the moving body has neither repugnance nor propensity to motion that takes it neither farther from nor closer to the center, and consequently there is no reason for any decrease in the power impressed on it. Moreover, the cause of motion is not a single one, which might diminish on account of the new action; instead there are two distinct causes, of which gravity attends only to drawing the body toward the center, and the impressed power to leading it around the center; therefore, there is no reason for an impediment.