Malebranch's search after truth, or, A treatise of the nature of the humane mind and of its management for avoiding error in the sciences : vol I : done out of French from the last edition.

CHAP. IX.

A Continuation of the same Subject.

I. A General Proof of the Errors of our Sight about Motion.

II. That it's necessary to know the distance of Objects, to judge of the swiftness of their Motion

III. An Examination of Means to know their distances.

TAke this General Proof of all the Errors we are liable to, in respect of Motion.

[illustration]

Let A be the Eye of the Beholder, C the Object which I suppose at a considerable distance from A, I say that though the Object remains immovable in C, he may believe it as distant as D, or as near him as B: and though the Object should recede to D, or ap∣proach to B, he might believe it immovable in C; on the contrary, although it approach towards B, he may believe it immovable in C, or receding towards D; And although the Object advances from C, to E, H, G or K, he may believe that it's only mov'd from

C to F, or I; On the contrary, although the Object were remov'd from C to F or ••, he might believe that it was mov'd to E, or H, or else to G or K. But if the Object be mov'd in a line equally distant from the Beholder, that is by a Circumference, whose Center should be the Eye of the Beholder, although the Ob∣ject move from C to P, he may believe that it moves only from B to O; and on the contrary, if it moves from B to O, he may believe it moves from C to P.

If beyond the Object C, there be another Object M which he believes immovable, although it moves towards N; or if C moves more slowly towards F, than M towards N, it will appear to move towards Y, and on the contrary, if, &c.

It's evident that the Proof of all these Propositions, except the last, in which there's no difficulty, depends only upon one thing, that is, we can't always make a certain Judgment of the distance of Objects, and if so, it follows, that we cannot know whether C is advanc'd towards D, or whether it approaches to∣wards B; and thus also of the other Propositions.

Now to see whether the Judgments we form about the distance of Objects are certain, we are only to examine the Means we are to make use of in judg∣ing; and if these Means are uncertain, we cannot judge infallibly, there are many of them, and they must be explain'd.

The first, the most general, and sometimes the most certain way, that we have to judge of the di∣stance of Objects, is the Angle, which the Rays of our Eyes make, whose point of Concurrence is, or measures, the Object; When this Angle is very great, we see the Object very near; on the contrary, when it is very little, we see it very distant; And the Change which happens in the Situation of our Eyes, according to the Changes of this Angle, is the means whereof our Soul makes use, to judge of the di∣stance or nearness of Objects; for even as a blind Man, who shou'd have in his Hands two streight Sticks, whose length he did not know, might by a kind of Natural Geometry, judge very near of the

distance of some Body, in touching it with the end of these two Sticks, by the disposition and distance of his hands: So it may be said, that the Soul Judges of the distance of an Ob∣ject by the disposition of its Eyes, which is not the same, when the Angle by which he sees, is sometimes greater, and sometimes less, when the Object is nearer, and when it is farther off.

We shall be easily perswaded of this, if we take the pains to make this very easie Experiment: Hang a Ring upon a Thread with the edge towards you, or else thrust one Stick into the Earth, and take another in your Hand, which shall be crooked at the end, go back two or three steps from the Ring or the Stick, wink with one Eye, and try to put the Stick in your Hand through the Ring, or to touch the other in the Ground traversly, about the height of your Eyes; you will be surpriz'd, not to be able to do that once in an hundred times, which you believe is so easie to be done. Now if you even lay by the Stick, and at∣tempt to put your Finger into the Ring, hanging with the edge towards you, you will find it difficult alt ho you were just at it.

But it must be well observ'd, that what I have said about putting a crooked Stick through a Ring, or touching another Stick traversly, will not hold, if the Eye be in a right Line with the opening of the Ring, for then there would be no difficulty in it; but it would be easier to effect it with one Eye shut, than with both the Eyes open, because that would guide us.

Now it may be said, that the difficulty which is found in hitting the hole of the Ring traversly, with but one Eye open, is owing to this, that the Eye be∣ing shut, the Angle, which I have spoken of, is un∣known; for to know the bigness of the Angle at the Eye, it is not sufficient to know the length of the Base, and one of the Angles at the Base, (unless the other be right) but we must also know the other Angle at the Base, or the length of one of the sides, which can't exactly be known, but by opening the other Eye: And thus the Soul cannot make use of its Natural Geometry to Judge of the distance of the Ring.

The disposition of the Eyes, which accompanies the Angle, form'd by the Visual Rays that meet in the Object, is then one of the best, and most Universal Methods, which the Soul makes use of, to Judge of the distance of Things: If this Angle then, does not ad∣mit of any Sensible Change, when the Object is near, if we approach to it, or recede from it; it will follow that the Method is false, and that the Soul cannot make use of it, to Judge of the distance of that Object.

Now 'tis very easie to know, that this Angle changes remarkably, when an Object that is but one Foot from our Eyes, is remov'd to four; if it be on∣ly remov'd from four to eight, the change is much less sensible, if from eight to twelve, 'tis still less; if from a thousand to a hundred thousand, 'tis yet less. Lastly, the change will be wholly insensible, if the Object were remov'd into the Imaginary Spaces; so that if there were a considerable Space betwixt A and C, the Soul could not, by this means, know whether the Object is nearer to B or D.

'Tis for this reason, that we see the Sun and Moon as if they were wrapt up in Clouds, althô they are extreamly distant behind them, and that we Natural∣ly believe all the Stars are at an equal distance, and that the Comets are fix'd, or almost without any mo∣tion, towards the latter end of their Course: As also, that they wholly dissipate after some Months, because they remove from us, in very near a right Line, to our Eyes, and lose themselves in the great Spaces, whence they return not till after many Years, or even after many Ages.

To explain the second way, which the Soul makes use of, to Judge of the distance of Objects, we must know, that 'tis absolutely necessary that the Figure of the Eye be different, according to the different distance of the Objects that we see; for when a Man sees an Object near him, it's necessary that his Eyes were more extended than if the Object were farther off, because, that to the end the Rays of this Object may meet upon the Optic Nerve, (which is necessary for

Vision) the distance between this Nerve and the Chrystaline Humour, must be the greater.

It is true, that if the Chrystaline Humour became more Convex, when the Object is near, it would have the same effect as if the Eye was more extended; but it's incredible, that the Chrystaline Humour can easily change its Convexity, and yet, on the other side, we have a very sensible Proof, that the Eye is extended, or drawn out in length: for Anatomy teaches us, that there are Muscles which encompass the middle of the Eye, and that one may perceive the Effort of these Muscles in compressing, or extending it when any Object is to be seen very near.

But 'tis not necessary to know here, after what man∣ner this is done, it's enough that it happens from the change of the Eye, whether it be, that the Muscles, that environ it, compress it, or whether the little Nerves, that answer to the Ciliary Ligaments, which keep the Chrystaline, Humour suspended among the other Humours of the Eye, do relax, to encrease the Convexity of the Eye, or contract themselves to di∣minish it.

For, in fine, the change which happens, be it what it will, is only to cause, that the Rays of Objects may exactly meet together just upon the Optic Nerve. Now 'tis manifest, that when the Object is five hun∣dred Paces, or ten thousand Leagues distant, we see it with the same disposition of the Eye, without any sensible change in the Muscles which encompass it, or in the Nerves which answer to the Ciliary Ligaments of the Chrystaline Humour; and the Rays of Objects meet very exactly upon the Retina, or Optic Nerve. Thus the Soul would Judge that Objects, ten thou∣sand, or a hundred thousand Leagues distant, are on∣ly five or six hundred Paces off, if it Judg'd only of their distance by the disposition of the Eyes, which I have spoken of.

However, 'tis certain that the Soul makes use of this means when the Object is near: If, for Example, an Object is but half a Foot from us, we distinguish well enough its distance, by the disposition of the

Muscles, which compress our Eyes, so as to extend them a little; and even this disposition is painful: If the Object is at the distance of two Foot, we yet di∣stinguish it, because the disposition of the Muscles is a little sensible, althô it is not any longer painful, but if we remove the Object to some considerable distance, this disposition of the Muscles becomes so insensible, that it does not in the least assist us in Judging of the distance of the Object.

These are two Means that the Soul uses to Judge of the distance of Objects, which are very useless when the Object is five or six hundred Paces distant from us; and which, also, are not certain, althô the Object were nearer.

The third Means consists in the bigness of the Image, which is Painted at the bottom of the Eye, and which represents the Objects as we see them. 'Tis granted, that this Image diminishes in proportion to the distance of the Object, but by how much the Object, that changes its distances removes farther off, by so much is the diminution less sensible: For when an Object is at some reasonable distance, suppose five or six hun∣dred Paces, more or less, in proportion to its magni∣tude, there arises very considerable alterations in its Elongation, without any sensible change in the Image which represents it, as is easie to be showed. Thus, also, this third Means has the same defect as the two preceding.

It may be further observ'd, that the Soul judges not of distant Objects, whose Image is Painted very small upon the Retina. For Example, when I see a Man, or a Tree, at the distance of a hundred Paces, or else many Stars in the Heavens, I judge not that the Man is more distant than the Tree, or that little Stars are farther off than the great ones, althô the Images of the Man, and little Stars, are Painted less upon the Retina than the Tree, or the great Stars.

Moreover, the bigness of the Object must be known to judge near of its distance; and because I know that a House is greater than a Man, altho' the Image thereof be less than that of a Man, yet I do not there∣fore

judge it nearer, imagine the same of the Stars, our Eyes representing them all at the same distance, althô it be very reasonable to believe some more di∣stant from us than others. Thus there are an Infinity of Objects, whose distance we cannot know, since there's an Infinity of them whose greatness we are ig∣norant of.

We also Judge of the distance of the Object, by the power whereby it acts upon our Eyes, because a di∣stant one acts more weakly than another; also by the distinction and clearness of the Image which is form'd in the Eye; because, when an Object is distant, its necessary that the Eye-sight dilate, and consequently, the Rays meet together a little confusedly: Hence it is, that Objects which are but a little distinct, or such as we see confusedly appear distant from us; and on the contrary, clear and distinct Objects appear to be near us. It's evident enough, that these last means are not proper to Judge of the distance of Objects with any certainty: I shall not insist upon the last of all, which is that that helps the Imagination, and which easily carries the Soul to Judge of very distant Objects.

The sixth and principle Means consists in this, That the Eye does not exhibit to the Soul an Object by it self, and distinct from others, but also all Objects ly∣ing betwixt us and that, which we consider.

When, for Example, we look upon a distant Steeple, we commonly see, at the same time, many in∣terjacent Fields and Houses, and because we judge of the distance of these Fields and Houses, and see the Steeple is beyond them, we judge also that it is very distant, and also greater, than if we saw it alone: However, the Image thereof, which is traced at the bottom of our Eye, is always of an equal bigness, whether there are Fields and Houses betwixt us or not, provided we see it at an equal distance, which is suppos'd. Thus we judge of the bigness of Objects by their imagin'd distance, and the Bodies betwixt us and the Object do much assist our Imagination in it, even as we judge of Duration, or the length of Time,

after some Action done by the remembrance of a con∣fess'd Series of Things, which we have done, or of Thoughts which we have successively had after this Action, for 'tis all these Thoughts and Actions which have succeeded one another, that assist our Mind in judging of the length or duration of some Time; or, rather, a confus'd remembrance of all the successive Thoughts about the same thing, is nothing else but our Judgment of Duration, even as a confus'd sight of the Fields, which are betwixt us and the Steeple, is the same thing as our Judgment of the distance thereof.

Hence 'tis easie to know, the true Reason why the Moon appears greater when it rises, than when it is much elevated above the Horizon, for when it rises it appears many Leagues distant from us, and even be∣yond the Sensible Horizon, or the Earth which ter∣minates our sight, whereas we judge it to be but about half a League from us, or seven or eight times as high as our Houses, when it is most elevated above the Horizon. Thus we judge it much greater when it is near the Horizon, than when it is very distant from it, because we imagine it much more distant from us, when it rises, than when is it very high.

It's true, there are a great many Philosophers, who attribute what I have said to the Vapours which rise out of the Earth: I agree with them, that Vapours, refracting the Rays of Objects, make them appear the greater. I know there are more Vapours betwixt us and the Moon, when it rises, than when it is risen very high, and consequently, it must appear some∣thing greater, than if it were always equally distant from us: However, it cannot be said that this re∣fraction of the Rays of the Moon, is the cause of these apparent Changes of its greatness, for this refraction hinders not, but that the Image which is traced in the bottom of our Eyes, at the rising of the Moon, is not less than that which is form'd there when it has been risen a considerable time.

Astronomers, which Measure the Diameters of the Planets, observe, that that of the Moon grows larger

in proportion to its distance from the Horizon, and consequently, in proportion to its appearing less to us; so that the Diameter of the Image, Painted at the bottom of our Eyes, is lesser when we see it greater. Indeed, when the Moon arises, it's more distant from us, by the Semi-diameter of the Earth, than when it is perpendicularly over our Head, which is the reason that its Diameter is greater than when it arises above the Horizon, because then it approaches to us.

That then, which is the cause of our seeing it greater when it rises, is not the refraction of its Rays, made by the Vapours coming out of the Earth, since the Image, which is form'd by these Rays, is then less, but it is the Natural Judgment that we make of its distance, because it appears beyond the Earth, which we see very distant from us, as was explain'd before, and I'm surpriz'd that Philosophers should look upon the reason of this appearance, and deceit of our Eyes, to be more difficult to find out, than the greatest Equations of Algebra.

This means of Judging of the distance of any Ob∣ject, by the Knowledge of the distance of Things, lying betwixt us and it, is of great use to us, when the other ways, which I have spoken of, fail us, for by this we can Judge, that certain Objects are distant from us many Leagues, which we cannot by any of the others, however, if we Examine, we shall find many defects in it.

For, first, this way serves only to Judge of Objects which are upon the Earth, and but very rarely, and for the most, very unprofitably, of Things that are in the Air, or in the Heavens. Secondly, we can't make use of it upon the Earth, but in things that are a very few Leagues distant from us. And thirdly, we must be assur'd, that there are betwixt us and the Object, neither Vallies, Mountains, or any such thing, which hinders us from making use of this means. Lastly, I believe there are none who have not had Experi∣ence enough, in this subject, to be perswaded that it is extreamly difficult, to make a certain Judgment of the distance of Objects, by a sensible view of Things

placed betwixt them and the Object: But I have en∣larg'd too much already upon this head.

These are the Means by which we Judge of the distance of Objects, we have observ'd considerable de∣fects in them, and may conclude, that the Judgments which are form'd upon them must be very uncertain.

Hence I can easily show the Truth of the Proposi∣tions which I have advanced. I have suppos'd the Object at C, considerable distant from A, then it may by many steps advance towards D or B, with∣out my knowing it, since I have no certain means to judge of its distance; it may even be suppos'd to recede towards D, when 'tis imagin'd to approach to∣wards B, because the Image of the Object is some∣times Painted greater upon the Optic Nerves, whether because the Air, which is betwixt the Object and the Eye, causes a greater refraction one time than ano∣ther, or whether it happens, sometimes, from the little tremblings of this Nerve; or, lastly, whether the Im∣pression which the imperfect uniting of the Rays, up∣on the Optic Nerve, are dispers'd and communicated to the parts which ought not to be affected with them, for it may happen from many different Causes. Thus the Image of the same Objects, being enlarg'd on these occasions, inclines the Soul to believe the Object is near: Suppose as much be said about the other Pro∣positions.

Before I conclude this Chapter, I must observe, that it much concerns us, for the preservation of our Life, to know well the Motion and Rest of Bodies, in proportion to their nearness to us; and that it sig∣nifies little, to have an exact Knowledge of the Truth of these Things, when they are remov'd to a great distance from us. This will evidently show, that what I have advanc'd in general about all the Senses, as that they do not help us to the Knowledge of Things, but in respect to the preservation of our Bo∣dy, and not according to what they are in themselves, is exactly true in this case; since we have a more exact Knowledge of the Motion, or Rest of Bodies, in proportion to their nearness: and which we cou'd

examine by the Senses, than when they are so distant; That the Relation they have to our Bodies ceases, as when they are five or six hundred Paces from us, if they are of an ordinary bigness, and even nearer than that if they are less; or, in fine, farther off, if they are greater.

Notes

• II. That it is necessary to know the distance of Objects to find the swiftness of the Motion.
• III. An Exa∣mination of the Means of knowing the distance of Objects.
• The Soul does not make all the Judg∣ments that are attri∣buted to it, th••se Natu∣ral Judg∣ments are only Sensa∣tions; and I only speak thus that I may better explain things.
• See the 4th Article of Chap. 7.
• The second way of Judg∣ing of the distance of Objects.
• The third Means to Judge of the distance of Objects.
• The fourth and fifth Means.
• The sixth Means to Judge of the distance of Bodies.
• See the preceding Figure.