SUMS

Dr. Kim H. Veltman

The Visual Process


1. Introduction
2. Extromission Theory
3. Intromission Theory
4. Point Theory
5. Possibility of Intersection
6. Intersection and Divergence beyond the Point
7. Small Objects in front of the Eye
8. Apertures and Contrary Movement of Objects
9. Single and Double Inversion
10. Models
11. Conclusions

 

1. Introduction

    In Antiquity, questions whether vision occurs through rays emanating from the eye, extromission, images coming to the eye, intromission, or some combination of the two had remained a matter for philosophical debate.1 Such questions were outside the scope of optics. As Hero of Alexandria explains in his Definitions:

Optics does not deal with physical questions and does not study whether given rays flowing ut from the eyes go forth to the boundaries of objects or whether images that are detached go forth from corporeal objects /and/ enter the eye along a rectilinear path or whether the intervening air is stretched or contracted by the ray-like pneuma from the eye.2

    Among the mediaeval Arabic writers on optics this attitude changed. Alhazen, writing in the early eleventh century, advanced demonstrations to show that vision occurs through a passive intromission of images.3 This became the dominant interpretation but alternative theories continued to hold their ground. Albertus Maganus, in his commentary on Aristotle's De sensu, notes no less than four explanations, each of which he ascribes to an ancient author:

a. emanation of visual rays (Empedocles);
b. emanation of visual rays which meet incoming rays (Plato);
c. intromission involving corporeal images (Democritus);
d. intromission involving spiritual images (Aristotle).4

    In addition Albertus Magnus alludes to, but rejects, a "somewhat new" theory claiming that vision involves a simultaneous extromission and intromission of rays. In the fifteenth and sixteenth centuries these competing explanations were perpetuated in the many commentated editions of Aristotle.

    At the same time Renaissance thinkers transformed their mediaeval sources. Alhazen had been one of the staunchest supporters of an intromission theory of vision. His sixteenth century editor, Risner, inserted a chapter (I:24) entitled: "Vision appears to be made by uvauy av, that is, rays that are simultaneously received and emitted." Through Risner, Alhazen could be seen to support a view he himself would have rejected.

    Even the landmark demonstrations of Kepler (1604) and Scheiner (1619) did not settle conclusively this debate concerning the visual process. In the mid-seventeenth century thre are still numerous debates in the universities on the question whether vision occurs through extromission or intromission.6 This context helps us to understand why Leonardo should consider alternative theories of vision in a manner that seems incompatible or even contradictory to a modern mind.

 

2. Extromission Theory

    On W19147-8v (K/P 22v, 1489-1490) Leonardo refers to combined extromission - intromission theory:

I state that the eye carries with it infinite lines that are attached to or united with the incoming ones which part from the objects seen.

    He pursues this theory on CA138rb (c. 1490):

Hence the eye sends into the air its similitudes to all the objects which are opposite it and in itself receives them, that is, on its surface, whence...the senso comune takes them and considers them and those which please it, it sends to the memory.

Whence I judge that the spiritual power of the species of the eye are produced going to the object, with the species of the object /going/ to the eye.

    On CA270vc (c. 1490) he explores this combined extromission - intromission theory at length in a scholastic fashion with a series of arguments and counter arguments, beginning with a general statement:

I hold that the visual power extends itself by visual rays to the surface of non-transparent bodies and that the power of these bodies extends to the visual power. And every similar body fills all the air in front with its similtidues. Each body of itself and all together does the same and not only does it fill it with...similitudes of form but also with their similitude of the visual power.

    He now gives an:

Example.

You see the sun when it finds itself at the centre of our hemisphere and the species of its form are in all the parts where it shows itself. You see the species of its splendour in all these same places and in addition there is joined the similitude of the power of heat and all these powers descend from its cause by radiant lines born in its body and bounded in opaque bodies without diminution of itself.

The North star continually stays with the similitudes of its power extended and incorporated, not only in rare bodies but also in dense, transparent and opaque bodies and it nonetheless does not diminish in its figure.

    One of the chief criticisms levelled against emanation theories of vision had been that the emanating object would gradually exhaust its resources. Leonardo's examples are clearly intended to counter this objection or as he himself puts it, these examples are:

    To confute:

...those mathematicians who say that the eye does not have visual power which extends beyond itself, for if it were so, it would not be without a great diminution in the use of the visual power and that if the eye were as large as...the body of the earth, it would accordingly be consumed in regarding the stars and for this reason they assign the eye as receiving and not sending anything forth from it.

    A further illustration follows to challenge those who exclusively hold an intromission theory:

Example:

O what will these say of the musk which always holds a great quantity of air filled in its odour and if one carries it a thousand miles and with that thickness of air, it will occupy without diminution of itself:

What will these say: that the sound of a ball made on contact of the clapper, which daily fills the countryside with its sound on its own, should consume this bell? Certainly it appears to me that such men are...but enough /of this/.

    He goes on to cite other cases which are almost certainly copied from an as yet unidentified mediaeval source:

Examples.

Is not that snake called the lamia seen the whole day by rustics which /snake/ attracts to itself as a magnet attracts iron with its fixed gaze, the nightingale, which with its lamenting song runs to its death.
Moreover, it is said that the wolf has power in its gaze to make men have hoarse voices.
Of the basilisk it is said to have the power of depriving every vital thing of life with its sight.
The ostrich /and/ spider is said to hatch its egg with its sight.

Maidens are said to have the power in their eyes to attract the love of men.

The fishes called Linno, some call it after St Ermo, which is found off the coast of Sardinia, is it not seen at night by fishermen, with its eyes in the manner of 2 candles, illuminating a great quantity of water and all those fish which are found in this splendour immediately come to the surface of the water, on their backs and dead.

    He continues with this theme of extromission on CA270vb:

How the radiant lines carry the visual power with them as far as their repercussion. Our soul (anima) or senso comune which philosophers assert is resident in the centre of the head...maintains its spiritual parts a long distance away from itself and this is seen clearly in the lines of the visual rays which, on terminating at the object, immediately give the quality of the form of their /inter/ruption to their cause.

Again in the sense of touch wh ich derives /from/ this senso comune, does one not see it extending with its power to the points of the fingers, which fingers, the moment they have touched the object, the sense immediately judges whether it is warm or cold, whether it is hard or soft, whether it is sharp or smooth?

    Having presented cases in support of extrmoission, Leonardo considers cases in support of intromission beginning with two examples involving a camera obscura:

How bodies...send...their form and colour and power outside themselves.

When the sun during an eclipse, remains in the form of /a/ lunar /crescent/, take a thin plate of iron and make a small aperture in it and turn the face of this plate towards the sun holding a sheet of paper at a distance of half a braccia behind this and you will see...the similitude of the sun on this paper in the shape of a lunar /crescent/ similar to its cause in form and colour.

Second example.

Again this plate of iron will do the same at night with the body of the moon and also with the stars. But from the plate of iron to the /sheet of/ paper there ought not to be any opening other than the little aperture and within the form of a square box, of which the face below and above and the 2 transverse /ones/ to the side are of solid wood and the /one in/ front has a plate /of iron/ and the one behind has a thin and white paper or parchment glued to the edges of the wood.

    As noted earlier (see above p. ) he illustrates such a box camera obscura on A20v (fig. 679, 1492). On CA270vb he also provides a:

    Third Example.

Again, having a tallow candle which produces an elongated flame and placing it in front of the said aperture, the said light will appear on the paper opposite in an elongated shape and similar to the form of its cause but inverted.

    This principle he illustrates on CA125vb (see above p. and fig. 694). In the final passage on CA270vb and the opening paragraph of CA270rb he returns to the theme of how objects can emanate images without exhausting themselves:

Quality of the sun.

The sun has body, figure, motion, splendour, heat and generative power, which things all depart from it without its diminution.

If you take a light and place this in a lantern tinted green or other transparent colours you will see by experience that all those things which are illuminated by this light appear of this colour of the lantern.

Again you may have seen in churches the light that appears in themt hrough the windows of /stained/ glass appears the colour of the glass of these windows.

And if this does not suffice for you, look at the setting sun when, through the vapours, it appears red /and/ tinges red all the clouds which take their light from this sun.

    He now gives his reason for citing these examples:

Opinions.

All these examples are made to prove how, all, or to be precise, many things exist which...together with the similitude of their form send the species of their power without injury to themselves.... This same can occur with the power of the eye.

    A scholastic type of discussion ensues with arguments in support of intromission:

Contrary opinions.

Again he who wished to say that the eye is not suited /to do/ other than receive similitudes of things without sending /out/ any power in return in the manner of the ear, this could be proved with the example of that aperture in a window which renders behind it the similitudes of the bodies that are as an object /in front of/ it. Hence one could say that the eye does likewise.

    An objection from the extromission camp follows:

Confutation.

If the alleged aperture, without sending anything outside itself other than its form, without visual power, renders the species of the object to colour and shape, and renders them interted, and the eye does the same, then everything should appear inverted to it.

    But in the next paragraph this objection is, in turn, dismissed such that the discussion ends in favour of the intromission theory:

Proof /to the/ contrary.

The circle of the pupil (luce) which appears in the centre of the white of the eye is of such a nature that it apprehends objects and this same circle has in it a point which appears black which is a perforated nerve which goes inside to the intrinsic power which is full of the power of the imprensiva and judgment which passes to the senso comune. Now the objects opposite the eye act with the rays of their species like many archers who wish to shoot through the bore of a light gun, in that he among the archers who is in a straight line with direction of the aperture of the light gun is more likely to touch the bottom of the aperture with the arrow. Hence objects opposite the eye will be passed to the sense in greater quantity to the extent that they are more in line with the perforated nerve.

The water in the cornea (luce) around the black centre of the eye acts like hounds in a chase who are the cause of flushing the (wild) game and then the greyhounds capture it.

So also with this because it is a humour which derives from the power of the imprensiva and sees many things but does not seize them. But all at once the central beam turns, which is in line with the sense and seizes the species and it confines those which please it in the prison of the memory.

    Hence Leonardo's only extended discussion of an extromission theory, ends with a defence of an intromission theory. His later notes leave no doubt that he favours a strict intromission theory of vision.

 

3. Intromission Theory

    From the time of Pliny8 supporters of the extromission theory had cited the example of nocturnal animals such as cats to support their claims. On CA90rb (c. 1490) Leonardo challenges such examples in order to establish a strict intromission theory:

On the nature of vision.

I say that vision is enacted in all animals by means of light and if anyone cites against this the vision of nocturnal animals, I shall say that this is equally subject to a similar nature, since it is clearly understood that the senses, receiving the similitudes of things, do not send forth any power from themselves. But through a mediation of the air which is between the object and the sense, it incorporates the species of things in itself and draws them to it by the contact it has with the sense.

Whether objects send spiritual powers to the ear and nose either by sound or by odour. This is unnecessary unless there is no light. The forms of objects will not enter through the air by similitudes if they are not luminous. It being thus the eye cannot receive from that air that which it does not have and that which /does not/ touch its surface.

If you wish to speak of the many animals which prey by night, I reply that when the little light which suffices for the nature of their eyes is lacking, that these help themselves with the power of hearing or smell, which /senses/ are not impeded by darkness and in which /power/ they far surpass man.

If you take heed of a cat, leaping among many jars and crocks by day, you will see that these remain intact and if you do the same by night, /the cat/ will break a number. Nocturnal birds do not fly unless a full or a partial moon is shining. Instead they feed between the setting of the sun and the complete darkness of night.

No object can be comprehended without illumination and shade. Illumination and shade are caused by light.

    A standard argument cited against extromission theories had been a time factor. If something is emitted from the eyes it would take time to reach the object and return to the eye.9 Yet we see objects without a time lag. Leonardo uses this objection on A81r (1492) to argue for a strict intromission theory:

It is impossible that the eye sends visual power outside itself through visual rays because in opening this first part, which would have to go from this beginning to the exit and to go the object, it could not do so without time. This being so, it could not in a month reach the height of the sun, if the eye wished to see it. And if it were joined it would be necessary that it continue the entire way that exists from there and that it always enlarged itself with the result that, between the sun and the eye, there would be composed a base and apex of a pyramid. Being thus it would not be enough even if the eye were a million worlds, that all this power is not consumed and if, for instance, this power had to pass through the air, as does odour, the winds would take it from its path and carry it to another place. And yet we see the body of the sun with the same spped as we see a distance of one braccio and it is not altered by the blowing of the winds or any other accident.

    In his arguments for intromission Alhazen had cited the example of after images.10 Leonardo uses this example on CA204ra (c. 1490):

Looking at the sun or some other luminous object and then closing the eyes, you will see it similarly at the back of the eye for a long space of time. This is a sign that species enter within.

    On CA204rb (c. 1490) he cites another demonstration to prove that the eye sees through intromission:

The ultimate experience giving a true opinion that a thing comes to the eye and not the eye to the thing, will be this.

It is clearly comprehended that when a single thing is seen by 2 concordant eyes, these eyes will refer it inside the head, to a single point as appears at mnop. But if you push one of the eyes with a finger you will see the one object that is seen convert itself into 2. You, who do not move the object, but move your eye, do not move the object seen, but move the similitude of that which is in your eye (when you move the eye). And if the eye sent forth visual power from itself, it could never happen that by moving the eye one would cause many rays such that the object appears to move /its/ position in accordance with how you move the object; whereas when I read, the letters seen appear to move their position in accordance with how one moves the eye.

    On A78 (1492) he notes: "Since effects often show the nature of their causes, I shall describe the nature of the eye with these and in what manner it receives within itself the species of objects." In the passage that follows he uses the experiment of a pushed eyeball to illustrate refractive properties of vision (see below p. ). Filarete, in the section of his architectural treatise devoted to perspective, had made an analogy between eye and magnets.11 Leonardo uses the same analogy on CA109va (c. 1490): "The air, the moment it is illuminated fills itself with infinite species of which the eye makes itself a magnet." He develops this analogy on A27r (1492) under the heading of:

Perspective.
The moment the air is illumined it fills itself with infinite species which are caused by various bodies and colours that are in front of it with respect to which the eye acts as a magnet and compass.

    In addition there are various passages where an intromission theory is implicitly assumed. On A36v (1492), for instance, he points out "All things send their similitudes to the eye through pyramids. On CU23 (TPL15, c. 1492), while comparing poetry and painting he again alludes to the intromission principle:

The imagination does not see with that excellence which the eye sees, because the eye receives the species or similitudes of the objects and gives them to the imprensiva and from this imprensiva to the senso comune and there it is judged.

    Another passage devoted to the comparison of poetry and painting, on CU21 (TPL2, 1500-1505) again alludes to intromission:

Why poetry places its things in the imagination of letters and painting gives them in reality outside the eye, which eye receives the similitudes not differently than if they were natural while poetry gives them without these similitudes and they do not pass to the imprensiva through the visual power as /does/ painting.

    Further allusions to intromission occur in his anatomical writings. On W19019r (K/P 39r, c. 1489-1510), for instance, he points out:

How the sense gives to the mind and not the mind to the sense and where the sense of the mind is deficient, the mind lacks in this life the notice of the function of this sense as is evident in a /person/ born mute or blind.

    On W19047v (K/P 48v, c. 1489-1510) he refers again to intromission:

If the spirit has articulate sound and if the spirit can be heard, what is hearing and seeing and how does the wave of a voice go through the air and how do the species of an object go to the eye.

    The theme is broached anew on W19045v (K/P 50v, c. 1489-1510):

And if you wished to say that it is the function of the eye to receive all the species of the infinite shapes and colours of objects positioned opposite it and /of/ smell...and the ear...we would say that the tongue also feels infinite tastes.

    On W19038v (K/P 80v, c. 1489-1510) intromission is again alluded to briefly: "the object moves the sense." The intromission question is broached at greater length on CA345vb (fig. , 1505-1508):

Whether or not a spirit can see bodies, not having to /do other/ than receive their species.

Let the visual power be at e, through which objects a /and/ b make their shapes recognizable through the lines ac and be. I state that /in the case of/ a man, the crystalline sphere n would suffice to send the received species to the spirit e. But necessity requires an /to be/ in a dark place.

    On CA345rb (c. 1508) he restates this idea as an assertion: "One does not see anything which does not send its species through the air." Seen as a whole these passages leave no doubt concerning Leonardo's position. In the early period he is aware of and cites various arguments in favour of the extromission theory of vision. But these he rejects and champions instead the intromission theory.

    It is easy to claim that images come to the eye. But what happens when they reach it and how do they pass from its surface to the brain?12 Leonardo has at least three basic solutions to this problem. He begins with an idea that the images converge to a single point and are there comprehended somehow by the visual power. At a second stage he considers the possibility that images converge to a point, intersect and then diverge again. This idea he at first dismisses because it would imply that images end up inverted within the eye. At at third stage he accepts that images are inverted at the pupil and asserts that they are inverted a second time by the crystalline lens. In his late notes he devises two clear demonstrations against the single point theory. We shall consider each of these stages in turn.

 

4. Point Theory (Stage One)

    In five passages Leonardo adopts the traditional theory that images converge to a point in the eye. Four of these passages are in Manuscript A (1492). A first reference occurs on A3r. Having defined "perspective," "pyramidal lines" and "point," he notes that "this point is that which, situated in the eye, receives all the points of pyramids in itself." On A10r he reformulates his basic definition of perspective and pursues the notion of a point in the eye:

By pyramidal lines I mean those which part from the superficial edges of bodies and lead to a single point by a distant concourse. Which point, in this case, I shall show to be situated in the eye, universal judge of all bodies.

Point, I say, is that which cannot be divided in any part. Now since this point situated in the eye is indivisible, no object will be seen by the eye unless it is greater than this point. This being the case it is necessary that the lines which come from the body to the point are pyramidal.

    An objection is now mentioned:

And if someone wished to prove that the visual power does not consist in this point, but rather in that black point seen in the middle of the pupil, one could reply to this person that a small object such as a grain of millet or panic grass or some other thing would never diminish and that thing which was larger than this point could never be seen entirely, as becomes apparent in the proof below.

    This proof begins with a diagram illustrating his opponent's argument (fig. ) which Leonardo then explains:

Let a be the visual power, let be be the concourse of the lines coming to the eye. Let c /and/ d be grains of millet within this concourse.

You see the reason why these never diminish with distance and /why/ the body mn cannot be com prehended entirely by these. Hence it is necessary that the eye has in it a single indivisible point to which converge all the points of pyramids departing from bodies, as appears below.

    He now draws his pyramidal solution to the problem (fig. ) which he explains in the text below:

Let ab be the eye. Its centre touches the point mentioned above. If the line ef is to enter as an image through such a small aperture of the eye, it must be confessed that a small thing cannot enter into a smaller th ing unless it diminishes and if it diminishes it is fitting that one attributes /this to/ a pyramid.

    The visual pyramid thus accounts for how large objects enter a small eye. On A36v this theme continues. He notes that the vanishing point will never be higher than the eye:

because the eye has in it this point to which are directed and to which converge all the pyramids carrying species of objects to the eye and this point always directs itself with the point of diminution /i.e. the vanishing point/ which appears at the limit of things seen.

    On A37v he pursues the problem:

As regards the point which comes to the eye this can be understood with greater facility, for if you look into another person's eye, you will see your image. Hence if you imagine 2 lines parting from your single point of all the images coming to the eye.

    But here he is citing an idea from Euclid's Optics (see above pp. ). He himself had, in the meantime abandoned the point theory.

 

5. Possibility of Intersection (Stage Two)

    By 1492 the term point has taken on another meaning for Leonardo. It is now potentially the point where lines of a converging pyramid intersect before diverging anew in intverted form. But if the iamges are inverted, why should the eye see them right side up? This difficulty troubles him and his first response on A77 91492) is to reject the point theory in a passage entitle:

    In the visual power the species are now reduced to percuss at a point.

And if you wished that they passed this point, one would need to confess that an intersection occurs which, by its nature, turns everything seen upside down. However, since things are only seen right side up, there is no point of intersection.

    Having rejected the theory on logical grounds, he provides a demonstration to prove that images cannot terminate at a single point:

And this is proven as follows: take a piece of straw and place it in front of the eye at a space of half a braccio and there judge it. Then if you move it back, the more you remove it, the more it diminishes, until it goes to nothing.

And if you draw it from this /distance of/ half a braccio towards the eye, the more you approach it, the more it will diminish. And if you touch the eye with it, you will lose it entirely through its diminution. If the eye saw with a point, this could not happen. Instead, the more you draw it near, the more it would increase.

    Directly beneath he draws a diagram (fig. ) and then explains why a piece of straw is experienced in this way:

Ad is the whole power of sight. Ik is a spherical body less than the pupil. Half of the pupil (luce) ab sees beyond this body to the points e /and/ g. The other half of the pupil sees beyond the space fh. Hence this pupil sees what is beyond the body or straw ik.

And by this /means/ one proves that the eye does not see through a point, but, through the concourse of the pyramids, creates a point at the centre of the pupil (luce) which does not belong to the function of the visual power. The above mentioned body will produce a darkness in the place eh similar to fog and this is because this part of the pupil cannot see gh and likewise cd cannot see the space ef and the point in the middle does not see the space fg.

    He now interjects an opposing opinion and refutes it:

The visual power can be in the body in the middle or and it can be at the triangle mn further back. No, because the pyramid mn which leaves the spherical body would invert all the species upside down, beyond it.

    Here it is logic that persuades him that there should be no intersection of images within the eye and this logic prevents his approaching the problem of image formation int erms of physics.

 

6. Intersection and Divergence Beyond the Point (Stage Three)

    Even so, by 1490, he has begun to consider seriously an alternative that images intersect, diverge, only to converge and intersect again. Two analogies persuade him to accept this possibility: one between the pupil and the camera obscura; a second between the crystalline lens and a sphere of water. This he illustrates on CA222va in three diagrams (figs. ), accompanying which he notes:

(figure)

Fig. 1120: Camera obscura demonstration which confirms how images converge to a point and then diverge anew on K/P 118r.

If the eye does not make a point, no minimal thing will ever diminish over any distance, and if it makes a point this is indivisible and in the indivisible part no species can be comprehended, since they are confused with one another and if the objects are seen well without confusion..., and every minimal object diminishes with distance, then it is necessary that the lines of the species make an intersection at a point and having passed this begin to diverge /again/.

    Here he accepts that images converge at a point, but now intends it in the sense of point of intersection. Similarly on Forster III 29v (1493) he states that "similitudes of bodies intersect in a point." The accompanying diagram (fig. 689) makes it clear, however, that the images subsequently diverge.

    This more complex meaning of point is also found in later passages. Hence one reason for his extended eulogy of the point on CA345vb (see above pp. ) is because images "can be reborn in such a small space and recompose in their dilation." And on W19149-52r *K/P 118r, 1508-1510) although he asks: "How do we conclude that the surface is reduced to a point?", the accompanying diagram (fig. 1120) reveals that the images diverge immediately beyond. Thus, after 1492, when he refers to images coming to a point, he frequently means something very different than in his early notes.

    This new concept of double inversion of images within the eye is illustrated in a number of diagrams. ON BM171v (1122, c. 1492) he is exploring the idea. On CA337ra (figs. 1144-1145, c. 1492*) his analogies between both pupil and camera obscura and crystalline lens and sphere are explicitly shown. These analogies underlie his later drawings on CA345vb (fig. 1150, c. 1508), K/P 118 (figs. 1154-1156, 1508-1510) and a series of alternatives considered on D2v, 3r, 3v, 8r, 8v, and 10v (figs. 1172-1178)

    *Pedretti, 1979, claims c. 1490. Since Leonardo explicitly denies the possibility of inversion on A77, (1492) it is unlikely that he would have made careful demonstrations of such inversion prior to this.

    Two experiences prompt this view. One is the camera obscura (see above pp. ). A second is refraction which leads him on BM221v (1500-1505) to claim that: "The concourse of lines created by the species of objects positioned in front of the eye do not converge to a point within this eye along straight lines." In addition he develops two demonstrations to counter the point theory.

 

7. Small Objects in Front of the Eye:A First Demonstration Against the Point Theory (Stage Four a)

    As early as 1490, on CA250va, Leonardo is exploring the how objects smaller than the eye are perceived, (see below pp. ):

Every transparent object between a /and/ e which is not a point but all the pupil is equal in its visual power, but not equal in strength because that part which is more distant from its centre, discerns things less. The visual power, being equally diffused throughout the pupil, no object of less quantity than it...positioned close to it, can occupy any part of a distant object.

    In defence of this claim a demonstration (fig. ) follows:

You will make the test as follows: let us say that cp is the /eye/; let f be the object less /than the pupil/ positioned in front; let ae be the distant object; draw the line oe to the opposite /side/ f and similarly the line nb. You see that the half pupil on sees all of b and similarly the other half sees ac and by this is demonstrated that if the point n only saw the first object f, this /object/ would occupy the entire part bc of the second object at the eye.

    This leads him to conclude:

Hence it is confirmed /that/ all the species of objects enter the eye upside down. After f you see b /which was/ above as being below at n and e /which was/ below /cor/respond/ing/ to c above.

    He reformulates this demonstration in terms of an attack (fig. ) on the point theory:

Proof how perspective, function of the eye, does not reduce itself to a point. The reason is this. If you place an object somewhat smaller than the pupil near the eye, you will see every object behind this occlusion as if the occluding object were transparent. Let us say that the pupil is op and that the point imagined by the perspectivists is n. Now if you position the quantity f opposite it, you do not see that the place bc is occluded by this f, whence the experience.

    He returns to this theme on K125/45/r (after 1504). Here he is content merely to draw the diagram (fig. ) and note that objects smaller than the pupil do not occlude objects beyond them. On CA237ra (c. 1500) he had redrawn the basic diagram (fig. ) and implicitly attacked the point theory:

The species of an object less than the eye do not converge pyramidally in this eye.

...The visual power is diffused with equal power in all the "pupil" of the eye...whence...the visual faculty is in all the "pupil" and all in every part of this.

    He attacks the point theory briefly on F28v (1507) (see below pp. and then at greater length on D6v (1508) where he begins with a general statement:

Of the human eye.

The pupil of the eye has visual power all in all and all in every part and the object opposite the eye smaller than the pupil will not occlude any distant object at the eye. And even if it /i.e. the object/ be dense, it functions as a transparent object.

    An adversary's claim is now introduced and countered:

Here the adversary says that the visual power is reduced to a point and from this it follows that every object positioned in front of the pupil which is larger than the point, will occupy the attention /of the eye/. I say that according to him, and if it were true that the visual power is reduced to a point, the convexity of the eye...which, with its parts, is turned towards a great part of the universe opposite it, would not be of such curvature if these /parts/ were not equidistant from this point and /these parts/ were not interesected at an equal distance from this point on its surface /such/ that each of these would correspond to the same real proportions in the intersections of the angles with the proportions of the similitudes of the bodies corresponding to this part.

    The attack continues with an appeal to experience:

To such /an adversary/ one demonstrates an experiment and then the necessity of such an experience and first for the experiment let there be placed in front of the pupil a quantity of an average sewing needle and let it be as close as possible and you will see that the information /notitia) about any object placed at any distance behind this (pupil) needle will be impeded. What I say is entirely in conformity with experience and necessity produces it, for if such a visual power reduced itself to a point, /then/ every minimal object placed in front of such a visual power would occlude information (notitia) about a large part of the sky, for if a large part of the sky sends the sepcies of its stars to the pupil, an object positioned nearby and equal to half of its diameter would occupy (a great part) nearly half of this sky. Whence Nature, because nothing is lacking to the eyes of animals has arranged...that this pupil has the least number of impediments...and the least number that is possible, by which the visual power would /otherwise/ be very greatly impeded for, as was said, every minimal object positioned in front would produce a great occlusion.

    Another example follows:

Again experience shows that chequered cloths made of thick horse hairs do not occlude anything beyond them and occlude less the more they approach the eye. Now if the visual power were in apoint the more these horse hairs approached, the larger would be the space that they would...occlude.

However, since experience does the contrary it is true that the visual power is diffused through all the pupil and every part in itself will function and sees beyond such horse hair, encompassing it, and seeing beyond the piece of their thickness and by necessity it causes pyramids close to the said hairs.

    He illustrates these situations in the right-hand margin. In the upper diagram (fig. ) he shows how a small object in front of the eye does not occlude objects behind it. The caption: "author," identifies this as his position. In the next diagram he shows how a small object occludes things beyond it if one assumes a point theory of convergence. The caption: "adversary" identifies this as the competing point of view. On E15v (c. 1513-1514) he returns once more to this demonstration:

On the eyes.
Among bodies smaller than the pupil of the eye, the one which is closer will be less known by this pupil. And with this experience we have learned that the visual power does not reduce itself to a point because if the etc...

    Here the text stops and we are told to "read in the margin," where the passage continues:

Here follows what was lacking below. But the species of objects which concur to the pupil of the eye are spread out over this pupil in the same way in which they are spread out in the air. And the proof of this is taught when we look at the starry sky without fixing the eye on one star more than on another, for then the sky is seen seeded with stars and they are proportioned in the eye as they are in the sky and their spaces are similar.

8. Apertures and Contrary Movement of Objects: A Second Demonstration Against the Point Theory (Stage Four b)

    Meanwhile, he had been developing a second demonstration against the point theory involving apertures and the contrary movement of objects. At first he merely sketches the problem in passing on CA112ra (1505-1508). Then he becomes puzzled by the phenomenon as is clear from a note on CA222vc (fig. , c. 1506-1508):

It is said that if the motion from n to m appears contrary to that from g to f, (and) it follows also that the motion from f to g should appear contrary in the eye, that is, from m to m and this is not confirmed by experience. Hence another proof is needed.

    He pursues this problem in the Manuscript K. On K127/47/v he begins by considering a stationary situation (fig. ):

It is possible that a (sole) same pupil sees a same object two times (in two places) at the same time.
The inferior part b of the pupil ab sees the object c occluding d and the superior part a of the same pupil sees the same object c occlude the surface gf beyond the aperture e in the position g. Hence the object c is seen at the same time at d /and/ g and this is what I wished to demonstrate.

    On K127/47/r he introduces the factor of motion into the discussion: "It is also possible that a same pupil sees a same object at a same (object) time make 2 contrary movements without alteration of this pupil." Beneath this he draws a diagram (fig. ) which he explains:

That which is proposed above is seen by a pupil when it...sees the air through a small aperture made in a /piece of/ paper by the point of a needle, and holding it close to the eye and interposing a very thin /piece of/ straw between the eye and the aperture which, when you move it /i.e. the straw/ from right to left the eye will see it in its true motion and its true position where it is in truth...and beyond this aperture it will see it more...contrary...to its true mo/tion/ such that it sees the true and deceptive movement separate from one another at the same time.

    This explanation continues on K126/46/(v):

And the reason is that, /since/ all vision is made by straight lines, /and/ the medium is uniform, the part a of the pupil sees o...beyond the aperture at s and it would be impossible, with such an aperture, to see it through abq at q and /along/ a non-straight line.... Hence let o be lowered to np. /Then/ one will see o at r and if o is lowered to m, then o will appear to the lower part of the eye c, which will have jumped to the extremity q.

    On K125/45/v he provides further details concerning the experiment:

In cases of motion...of the object between the eye and the aperture of the paper you need to make the perforations with very minute apertures and draw the thing that moves which is slender as the point of a needle and in moving let it touch your eye brows and let the paper be moved to a distance 1/4 braccio from the eye and through the apertures one sees the air.

    On K126/46/r, he adds: "But if the motion of the object be above the perforated paper then the eye will see the true motion of the object." Beneath this he adds a diagram (fig. ) and a text "let us say that a moves through abc: which then breaks off. On D2v he returns to this problem:

Of the human eye.

How the sepcies of some bodies which pass to the eye through some aperture impress themselves upside down on its pupil and the sense sees them upright.

The pupil of the eye which, by means of a minimal round aperture receives the species of bodies positioned behind this aperture...always receives them upside down and the visual power always sees them as right side up as they are and this occurs because the said species...pass through the centre of the crystalline sphere positioned in the centre of the eye...and in this centre they unite at a point and then dilate at the opposite surface of this sphere, not departing from their straightness and at such a surface the species are directed in accordance with the object where they are caused and from there they are taken up by the imprensiva and sent to senso comune where they are judged.

    This process he illustrates in the upper right-hand margin (fig. 1142) and then describes in the text:

Let this be proved...as follows. And let the pupil be an of the eye kh and let the tiny round aperture be p /which is/ made in the paper with the thin point of a style. And let the object positioned in front of this aperture be mb. I say that the superior part of this object cannot come to the superior /part/ of the pupil of the eye along the straight line ma because at v its transit is impeded through the interposition of the paper. But this upper extremity m passes along a straight course through the aperture to the inferior part n of the pupil or, if you wish, of the crystalline sphere, and from there it directs its course to the centre of this sphere and is raised to the superior part of the opposite side and from there passes to the senso comune as I have said.

    Beneath the first diagram in the right-hand margin Leonardo redraws a detail (fig. 1143) followed by a caption "crystalline sphere placed in the centre of the eye" and a marginal note: "Here it is presupposed that the pupil has visual power in every part of it side and this is so in effect and without this every demonstration is ruined." Below this he draws an other diagram (fig. ) which he numbers "2e" and then describes in the accompanying text headed:

Here below is demonstrated the experience from which originates the certainty of such a new investigation.

The gd be the eye of which the pupil ap sees the object tc through the aperture q (made in the paper rs). I say that if you...move the style lq from above to below the pupil near this pupil along the line kh which appears beyond this aperture q, that such a motion of the style will be contrary to its true motion and the reason is that touching the style is the line ac /which/ touches both the highest...line, which is on this side of the aperture q, and the lowest which is beyond this aperture. And thus continuing the descent on this /near/ side of the aperture in front of the pupil with your style, you mark the contrary beyond this aperture, because if you descend on this /near/ side with the fronts of the lines amnop all will rise beyond at the ends of the lines cyxvt. Hence the style which touches the line ac occludes the site c and if you descend to the line n with such a style you occlude the site y beyond the aperture and thus it continues to the end of the motion.

    On D4v, this experiment is used to attack the point theory. Under the heading: "Eye of man" he begins with a claim:

That it is true that every part of the pupil has visual power and that this power is not reduced to a point as the perspectivists would wish, that is, that all the species of objects come to the eye through pyramids and...are reduced to an angle in which the judgment of the thing seen is made. Here experience shows that the contrary is true.

    A draft description of his needle experiment follows:

And this is experimented as follows. LEt an aperture about the size of a millet seed be made by a large needle in a /piece of/ paper and let this paper be positioned opposite the pupil of the eye at a space of 1/3 or 1/4 of a braccio and through this aperture rlook at the air pq. Then interpose this needle or some other similar straw between the pupil of your eye and the said aperture of the paper. But makde /sure/ that such a needle is close to the eye...in such a way that it touches the points of its eyelids. Then move this needle up and down and to the right and left in front of your pupil and in the air beyond this aperture you will see clearly that the similitudes...of this needle make all the contrary movements to those which you make with the needle /in the space/ between the eye...and the said aperture.

    Why this should happen the explains:

The cuae of that which was said above occurs because the visual power is spread throughout all the pupil of the eye and in every point of this one recognizes the images of the objects positioned opposite this eye which, if it were not so, the experience would not occur.

    He now reformulates this experiment (fig. ) in greater detail:

Let this be proven as follows. Let the circle st be placed for the pupil of the eye. Let the paper, 1/3 braccio distant from the eye, be abcd in which there is made an aperture r, the size of a millet seed. Let n be the size of a needle placed as close as possible to the eye, which /needle/ moves in front of this aperture r from n to m in slow motion. Now you will see the image of this needle move in the air beyond this aperture from q to p, that is, in contrary motion, and this occurs because, in the beginning of such movement, /while/ the needle...is above at n, its image passes through the aperture r and occludes the air in the part below at q and when the needle descends from n to m, its image in the air rises from q to p and the intersection of the straight lines of such a species or, if you wish to say, the shadow of such a needle, will always be made at g, and thus every motion made by any aspect beyond such an aperture is switched such that, if the visual power were not in us you would not see the image of this needle at q and if it were not at t you would not see it at p and the same is understood /to be the case/ in every part of such a pupil.

    In the right-hand margin he draws three diagrams: one (fig. ) which merely shows the inversion principle of all apertures; a second (fig. ) which illustrates the experiment just described and a third (fig. ) which shows the adversary's claim outlined in the marginal note beneath:

The adversary states that such vision is made in an angle, that is, in a point, and that this point will do the same. And if you experiment with what happens to the needle with the aperture of the paper and if you do not posit otherwise and say, let the point r be in the pupil vx/and/ let chgl be the paper in which is made the aperture t. Let the needle which descends to n be a and its similitude will be seen to move beyond this aperture also and it will move from uf and rise to m. To him one replies that he has not held in mind the 9th* of the first in which it is stated that all vision occuring in the eye through a same medium made along a straight line to the needle a opposite the point r will occlude the point m through the straight line rm. And when it will have descended from a /to/ n it will have occluded the point f along the straight line rf. Hence we have concluded what we proposed.

    This demonstration against the point theory helps him to account for the unclear boundaries of nearby objects (see below pp. ).

 

9. Single or Double Inversion in the Eye

    If vision does not occur through images coming to a point, how is it that the eye sees? Among Leonardo's earliest explanations of this problem is a passage on CA85va (fig. , 1503-1504), where he asks:

In what way the eye sees the things placed in front of it?

Let us posit that this ball drawn above is the ball of the eye(s) and that the lesser part of the ball, divided by the lines st, is the cornea (luce) and that all the things mirrored on the middle of the said cornea immediately run and go to the pupil, passing through a certain crystalline /i.e. aqueous/ humour which does not occlude things in the pupil which are demonstrated to the cornea and this pupil, receiving things from the cornea immediately refers them and sends them to the intellect along the line ab.

    Accurate vision, he claims, is only possible along the central line of sight:

And you know that the pupil does not send anything perfectly to the intellect or the senso comune except when the things given it by the cornea (luce) are directed along the line ab as you see the line ca does. And although the lines mfg are seen by the pupil, these are not considered, because they are not drected along the line ab.

    He supports this claim with a demonstration familiar to the optical tradition:

And the proof is this: if this eye which /is/ above would like to enumerate letters placed in front of it, it will be fitting that the eye turns from letter to letter, because it would not discern it, if it did not direct it along the line ab, as does the line ca, and the p, all things seen come to the eye by pyramidal lines and the point of the said pyramid makes its terminus and end in the centre of the pupil as drawn above.

    Here Leonardo appears to accept a theory that images concerge to a point but at the same time emphasizes the role of a central ray (see below pp. ). If the central ray along is held responsible for vision, then it is not necessary to consider the inversion of images and there is no problem of explaining why the eye should see inverted images as being right side up.

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Figs. 1121-1124: Early theories concerning inversion of images in the eye on BM171v.

    By 1492, however, he is exploring an alternative, namely, that images are inverted twice within the eye. Two analogies underlie this new theory. He notes that both a camera obscura and a sphere of water invert images. By anlogy, he assumes that images are inverted by the pupil, reinverted by the crystalline lens and are therefore seen in an upright position. The explanation furnished by these two analogies is basically simple. Even so Leonardo is not content with a de fgacto answer. He is continually changing his mind about precisely where in the eye the two inversions take place. For this reason it is necessary to examine in detail his various notes concerning double inversion within the eye.

    On BM171v (1492), for instance, he draws a sketch how light is inverted in passing through an aperture (fig. 1121) and directly beneath he illustrates an analogous inversion (fig. 1122) when images pass through the aperture of the eye. In the text opposite he discusses the camera obscura principle:

All the images of objects which pass through a window from the open air to the air confined by a wall are seen in an opposite position and that thing which will move from east to west in the open air will appear of contrary movement as a shadow on the illumined wall of the confined air.

    What happens to images once they have been inverted by a pupil, which functions as a camera obscura, remains a problem for him. In his diagram (fig. 1122) he shows how the rays diverge and then, for no apparent reason, begin converging again until they interesect a second time at the posterior border of the eyeball, before entering the imprensiva. In a third diagram (fig. 1123) he draws a tube-like nerve which extends to the pupil. This idea he develops in a fourth diagram (fig. 1124) in which the nerve is expanded to show a series of inversions caused by continual refelction. The nerve continues beyond the eyeball and connects with a container marked imprensiva. Although the location of the imprensiva is clearly marked in the diagram, Leonardo's text confirms that he is troubled concerning its precise whereabouts:

What is seen.

If the imprensiva were outside the eye it would be necessary that straight lines do not occur. For although b comes to eye f along a straight line and although it goes from f to d, nonetheless, the line which goes to the imprensiva remains straight and oblique. Therefore it is necessary that the imprensiva is in the eye. The nerve which parts from the eye and goes to the brain is similar to perforated nerves which, with infinite strands, interweave the skins of bodies and by their cavity, it is carried to the senso comune.

    In the course of 1492 he studies more carefully physical models which could account for the double inversion that he beleives occurs in the eye. Hence on CA125vb he explores both the inverting properties of a camera obscura (fig. 694) and spheres of water (figs. 1126-1132). On CA125va this theme is pursued. In the upper right-hand corner he again draws a sphere of water (fig. 1139) beneath which he explains:

(figure)

Figs. 1137-1143: Inversion of images in spheres of water and in the crystalline lens. Figs. 1137-1139, CA125va; figs. 1140-1141, CA133va; figs. 1142-1143, D2v.

Here the images of ab, pasing through the centre n are inverted at cd and the shadow goes directly from ua to c and from b to d and having passed s it will turn upside down to rt and let p be the light.

    In the lower right-hand column of CA125va (1492) he contracts the perception of far off and nearby objects:

The eye therefore sees far off objects as right side up and the aperture of the pupil, through the intersection of the species made in it, turns them upside down, whence the eye sees them as right side up from afar and those from nearby, touching the pyramid of the intersection appear in contrary motion.

    Alongside this passage he draws a diagram (fig. 1138) showing a first inversion behind the pupil and a second inversion behind the sphere of the crystalline lens. On CA222va (c. 1490[P] but probably 1492) this theme is pursued. He mentions how all lines come to a point in the eye and then diverge again (see above p. ), adding:

and being thus, if the imprensiva were in this divergence, every object would appear upside down. Not appearing thus, it is necessary that the said species pass through a spherical and transparent body which again inverts behind it, in a contrary way to that which was given in front of it which, by its nature, all the things which are given to it from one side, it turns them from the opposite side, upside down, and if the imprensiva is here, then you can see the objects well. Now place the mind inside the eye and you will see /how/ necessity, the master of all things, is well provisioned /and/ you will see that the eye has within it the instruments necessary for its function.

(figure)

Figs. 1144-1145: Model and model eye on CA337ra.

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Figs. 1146-1150: Inversion in the eye on CA345vb.

    Beneath this passage, in the right-hand margin he draws a rough sketch (fig. 1151) showing double inversion of images produced ;by a pupil acting as a camera obscura and a crystalline lens as a sphere of water. In the lower right-hand corner he redraws the diagram (fig. 1152) and then once more (fig. 1153), accompanied by a brief text:

That species of an object which falls on the surface of the eye between equal angles, will be well seen as b.
And that which falls between angles which are less equal, is less seen, as ac.

    On CA337ra (fig. 1144, c. 1490) he develops his analogies between both pupil and camera obscura and between crystalline lens and a sphere of water. Here the drawing is so precise that it has the appearance of an actual model. Had he actually placed his eye in front of a ball of water in a camera obscura, however, he would have experienced only a single and not a double inversion of images.13 In the upper part of CA337ra (c. 1490) he integrates his double inversion principle within a schematic adaptation of the eye (fig. 1145).

    On CA345vb (c. 1508), where he also discusses the camera obscura (see above pp. ), he returns to this problem of double inversion in the eye. Under the heading: "Whether or not the spirit can see bodies, having only to receive their species" he again draws the crystalline lens in the form of a sphere of water (fig. 1150) beneath which he explains:

Let the visual power be at e through which the objects ab make known their figures mediating the lines ac and be. I say that for a man the crystalline sphere n would suffice to send the received species to the spirit e, but necessity requires that an is in a dark place.

(figure)

Figs. 1151-156: Theory of double inversion in the eye. Figs. 1151- 1153, CA222va; figs. 1154-1156, K/P 118r.

    To the left of this passage he sketches three further visual hypotheses concerning the path of rays within the eye (figs. 1147-1149). In a first sketch (fig. 1148) some of the rays are inverted just beyond the pupil and then stop short at the crystalline lens. Other rays pass directly through the eye without inversion. In a second sketch (fig. 1147) directly beneath this he again shows some of the rays as being inverted while others penetrate the eye without inversion. A third sketch is more developed (fig. 1149). Here he shows how some rays come from an object, are refracted by the cornea, pass through the pupil, are inverted, refracted a second time at the crystalline lens and then converge to a point. In addition he draws other lines directly from the object to this point of convergence in the eye, probably to contrast the geometry of the situation with the realities of refraction. A note directly beneath this sketch confirms that Leonardo intends to study this problem mroe carefully in terms of anatomy:

Write in your anatomy what proportion all the diameters of all the sphere of the eye have and what distance the crystalline sphere has from them.

    He pursues the question of double inversion in the eye on W19150v (K/P 118v, 1508-1510):

Necessity has provided that all the species of bodies positioned in front of the eye intersect in two places, of which one intersection is generated inside the pupil, the other inside the crystalline sphere. Which, if it did not do so, the eye could not see so great a number of things as it sees. This is proved because all intersecting things generate such an intersection in a point. Since nothing is shown of bodies except for their surfaces, the boundaries of these are lines, by the converse of the definition of surfaces and every minimal part of a line is equal to a point, because niminal is said to be that thing, than which nothing can be less and this definition is the same as the definition of a point.

    Hence it is possible that the entire circumference of a circle sends its cimilitudes to its intersection as is shown by the fourth of this which states that all the minimal parts of species penetrate one another without occupation of one another.

(figure)

Figs. 1157-1161: Sketches concerning vision on CA222ra.

    In the right-hand margin he writes "These demonstrations are as an example of the eye," and sketches a first inversion caused by the pupil (fig. 1154). Below this he makes a more detailed drawing (fig. 1155) showing how an object ab is first inverted by the pupil at c and then by the crystalline sphere at q in order to appear right side up at rs. A summary text follows:

He species of so minimal an object penetrates the eye but that it is turned upside down and in penetrating the crystalline sphere it is again turned upside down and thus the species are returned right side up within the eye, as was the object outside the eye.

    Below this he draws another rough sketch (fig. 1156) of double inversion within the eye, and three sketches which appear to show the refractive properties of a flat (fig. 1014), convex (fig. 1015) and concave surface (fig. 1013) respectively. He also illustrates the inversion principle within a camera obscura (fig. 705, see above pp. ).

 

10. Models

    As early as 1490 Leonardo had become concerned with producing physical models of the eye. On CA222ra, for instance, (figs. 1157-1161) he notes:

(figure)

Figs. 1162-1164: Models of the eye. Figs. 1162-1163, CA297va; fig. 1164, CA141rbc.

If you take a hemisphere of glass and put your face inside it and close it well at the conjunction of the face, and fill it with thin (sottile) water, you will see all those things which are seen from the surface of this ball in such a way that you could see behind the shoulders.

    A diagram on CA141rbc (fig. 1164, c. 1490) might well show a model eye. By 1508 he returns to the problem. On CA190vb, for instance, he drafts two diagrams of the eye (figs. 1074-1075) accompanying which he notes:

"Make such an eye large and of glass like a natural one."

    In the Manuscript D he goes further. In a marginal note on D2v (1508) he recommends:

Let there be found an instrument that makes the same effect by necessity and thus you will have found the true interior shape of the eye.

    Preliminary instructions concerning such an instrument are given on D7v in the lower right-hand margin (fig. 1165):

Make spherical ampullas like this and then out them as one cuts glass with hot iron /held/ in a vice and make them into hemispherical shells like this and then make your spectacles (ochiali) filled with water like this and fill one only full of water.

(figure)

Figs. 1165-1169: Models of the eye. Figs. 1165-1168, D7v; fig. 1169, D3v.

    In the upper portion of this margin heoutlines further possibilities:

Break a decanter of glass and from the convexity and concavity you will make a mask filled with water and you will see that which is promised below and it will serve.

    This he illustrates in a diagram (fig. 1168) showing a man with his face immersed in such a mask with water. He also notes: "And if you wish to see with a single eye make it with the body of a small or large ampulla, etc." To illustrate this alternative he draws two further diagrams. In the first of these (fig. 1166) an eye is immersed in "tepid water" and as the caption explains: "Here the air makes itself a concave mirror." In the second diagram (fig. 1167) the form of the ampalla is reversed. As the caption explains: "here the air makes itself a convex mirror." The idea of a mask of water, mentioned on D7v is developed on D3v (fig. 1169) under the heading:

To make an experiment how the visual power will function as instrument of the eye.

In order to make an experiment on the way /that/ the visual power receives the species of objects from the eye, its instrument...let there be made a glass sphere five-eights of a braccio in diameter and then let so much be cut from one side that one can place the head in it /up/ to the ears. Then, inside, at the bottom let there be placed a floor of wood a third of a braccio which has as its centre an aperture...four times as large as...the pupil of the eye or approximately so, which makes no difference.

Moreover, let there be made a sphere with thin (sottile) water,...a sixth of a braccio in diameter. And having made this, fill everything with tepid and clear water and put your face in this water and look at the sphere and observe and you will see /that/ this instrument sends the species of st to the eye as the eye sends them to the visual power.

    He illustrates this model in the right-hand margin (fig. 1169) and beneath it adds the caption: "Tinge the larger glass /sphere/ on the outside and you will make the uvea." In his model he requires that the pupil be "an aperture...four times as large as is the pupil" but then adds "or approximately which makes no difference." The model is clearly intended to simulate only the inversion he assumes occurs in the crystalline lens. Hence he sees no contradiction between the single inversion shown in this diagram and the double inversion in the drawing of the eye alongside (figs. 1169, 1171).

    While fascinated by models, he does not insist that they should give a perfect simulation of reality. This separates his attempts from the model eyes of seventeenth century individuals such as Scheiner and for the experimental method codified by Galileo, Huygens and Newton. Even so Leonardo's efforts are of great significance because they shift questions of the visual process, from the realms of abstract philosophical debate to the domain of concrete physical problems which can be reconstructed through models and simulated experimentally. For this reason it is useful to trace the development of his ideas in detail. Directly beneath his model eye on D3v he draws a conceptual version (fig. 1171) which he carefully letters and then describes in the text alongside:

Here it is posited that the visual power is at the extremity of the optic nerves of which hm is one. Hence let us say that the visual power m cannot see an object a to the left of this left side unless...the ray...of the species of such an object pass through the centre of the two spheres, that is the sphere of the cornea (luce) dke and the sphere of the vitreous humour /i.e. the crystalline lens/ xytv and thus the path of the ray will be /along/ ae /to/ r /and then/ to vzx. Hence the visual power m will see an object a on the left being represented at x and thus the instrument of the eye cannot render such an object on the left to its same position except by way of...two intersections which pass through the axis of the eye as is demonstrated.

    By now he is convinced that double inversion is the only means of accounting for the visual process. Beneath his diagram (fig. 1171) he adds a marginal note pertaining to anatomy:

The pupil is black...because the uvea which is black is mirrored in the crystalline sphere which is in the centre of the albugineous sphere /i.e. the vitreous body/ and also appears blacker because the light of the air cannot illuminate...the albugineous sphere through so small an aperture as that of the pupil of the eye.

    He is still not content with his model of the eye and in the lower right-hand corner draws further diagrams (figs. 1170, 1172). In a first draft (fig. 1170) he increases the size of the crystalline lens relative to the sphere of the eyeball. In his second draft (fig. 1172) he carefully marks each of the parts with letters but then makes no reference to these in the text that follows:

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Figs. 1170-1172: Theories concerning the visual process on D3v.

The vitreous sphere /i.e. the crystalline lens/ is positioned in the centre of the eye in order to direct the species intersecting behind the aperture of the pupil such that those on the right return to the right and /those on/ the left return to the left after the second intersection which they make at the centre of this vitreous sphere /i.e. crystalline lens/.

    In the examples considered thus for Leonardo has assumed that a first intersection occurs at the pupil and a second intersection at the centre of the crystalline sphere - which he sometimes terms vitreous body. In a larger diagram near the centre of D3v (fig. 1175) he considers a new alternative. As in previous cases a first intersection at c is caused by a pupil which functions as a camera obscura. The rays ov and or then diverge until they arrive at the crystalline lens where they are refracted to a converging path. On emerging from the lens at p and q, the degree of convergence is again increased due to refraction and the rays cross a second time at n just prior to impinging on the sides of the optic nerve at h and k. To the left of this diagram he adds a short note:

Experience shows that pq is 1/3 of tv and since pq receives that which is given it* by tv, to the extent that tv is restricted, to this extent the angle /at/ o becomes smaller.

(* reading li e dato instead of lietato.

    Beneath this diagram on D3v a further explanation follows:

How the species give themselves to the visual power by two intersections of necessity.

(figure)

Figs. 1174-1174: Theories concerning the visual process on D3r.

The object a sends its image to the visual power by the...line ar to the part r of the cornea (luce) edf which then enters by the pupil at o and makes the intersection at o and passes through the vitreous sphere at v and penetrates this sphere on the side vq and passes through the intersection n and terminates at k, at the front of the optic nerve khl from which it is then referred to the senso comune.

    He now draws a bracket to indicate the end of a paragraph and considers the arguments of an adversary:

Here the adversary says that the intersection n does not take place but serves that of the optic nerves and that the pyramid n is intersected at the front by the optic nerve where small objects are made larger.

    On D3r he pursues this theme of two necessary intersections within the eye. In the upper right-hand margin he draws a more detailed diagram (fig. 1174) which he explains in the text alongside:

How objects on the right do not appear on the right if its species do not pass through two intersections.

The object k, joined to b, the surface of the cornea (luce) of the eye (which) gives itself to the visual power by two intersections, that is, n /and/ s, first entering from b to the pupil d and from d to f.

    There follows an explanation how refraction delays the intersection of the rays:

And it would pass through the intersection h /at/ the centre of the sphere of the cornea, that is, /at the centre of/ laby, but it first meets the crystalline sphere before it terminates its pyramid cdn. In this percussion such a pyramid cdn is cut in ef where the base of another pyramid is generated, i.e., efo and the sides of this pyramid intersect at o (and the image rs) and pass to the opposite part of the vitreous sphere /i.e. crystalline/ and f on the right makes itself left at uq and e on the left makes itself right at r.

    Next he describes the second intersection in the eye:

Then the second intersection is made at us, that is, that the vitreous sphere casts its pyramid (v)qrs and r on the right passes through the intersection s and makes itself left at i and q on the left makes itself right at g. And by the means the eye, /as/ instrument, brings the object on the right as right and the left as left to the beginning of the optic nerves.

    In the right-hand margin he draws another diagram (fig. 1174) with an alternative set of intersections. As he explains this is:

A second opinion with the same two intersections.

It is not denied that...all the sepcies which come to the surface of the cornea anb (do not) pass through the pupil cd as /was/ proved, and it is also conceded that all the lines of these species which pass to the centre of the sphere which begins with the said cornea (luce) are switched from right to left and from left to right such that a /on the/ right having passed e, the centre of the sphere of the cornea makes itself left at t and b makes itself right at r and grows dramatically because all the space ab comes to rt and this rt receives a size which appears similar to ab as is proved in perspective.

    At this point he draws two strokes (//) to indicate a new paragraph:

(figure)

Figs. 1175-1176: Late theories concerning the visual process on D3v and D8v.

Moreover, it is not denied that the vitreous sphere (i.e. the crystalline lens/ etkh renders it directly, in front of the pyramid khr and then reverses it after the intersection of the sides of such a pyramid at the points g /and/ l. Hence a on the left will make itself right at t after the...first intersection and will descend on the left until k and will pass through the 2nd intersection r and return to the left at the point g.

    The explanation on D3r involve alternatives which Leonardo implicitly rejects. He had put forth his own explanation of the visual process on D3v. To this he returns in a diagram (fig. 1176) on D8v. Here there is no explanatory text. But on D8r he redraws the diagram (fig. 1177) and adds the caption "sc is 1/3 of md," which refers to the size of the image emerging from the crystalline lens. On D3v he had referred to the same ratio. Beneath the diagram and caption on D8r, he adds a marginal note in which he dismisses the alternative explanations which he had considered on D3r:

You might perhaps say, that if the angle c of the pyramid bnc had a considerably narrower base, that the angle c would descend considerably lower and could perhaps descend to such an extent that it would enter the vitreous sphere and could not then intersect again on the surface of this...vitreous sphere. To which matter it is replied that in this case nature has provided well, such that when similar cases occur, the pupil contracts and enlarges depending on whether it has to consider universal or particular things or /those that are/ twoo luminous are too obscure.

    In the main text he gives his own version of the visual process:

The species of objects placed opposite the eye pass to the vitreous sphere /i.e. the crystalline lens/ through the...gate of the pupil and intersect behind this pupil...in such a way that the vitreous sphere/i.e. the lens/ is percussed on its left side by the right ray of the right sphere and thus it acts from the opposite side. Then it penetrates this vitreous sphere /i.e. the lens/ and the rays go on contracting and find themselves more narrowed when they are at the opposite side of this sphere than when they percuss it at the beginning.

    He interjects an explanation why refraction occurs at the lens:

And this restriction originates because the rays of species are drawn towards the perpendicular when they pass from the rare to the dense and here the albugineous humour is much rarer and subtler than the space included by the surface of the vitreous sphere /i.e. crystalline lens/.

    His explanation of the visual process now continues:

Thereafter, it /i.e. the image/ should enlarge again on returning to this albugineous /humour/, but it does not observe this rule because it is constrained to obey the nature of the vitreous sphere,...from which it emerges, where it passes to the albugineous humour (and) for this /reason/ it makes a pyramid in leaving the vitreous sphere and passes through the albugineous and intersects its sides at the point f and passes to the visual power g at the extremity of the optic nerve gs.

    To clarify the nature of the first intersection in the eye he draws a camera obscura in the lower right-hand margin (fig. 698) which he explains in the main text:

(figure)

Figs. 1177-1178: Leonardo theory of double inversion within the eye on D8r and D10v.

How the species of objects received byt he eye intersect within the albugineous humour.
The experience which shows that objects send their species or images intersected in the albugineous humour within the eye is shown when the species of illuminated objects penetrate through some small round aperture in a very dark habitation. Now you will receive these species on a white /piece of/ paper...placed inside such a habitation, somewhat close to this aperture, and you will see all the aforesaid objects on this paper with their proper shapes and colours, but they will be smaller and upside down as a result of the said intersection. These images if they originate in a place illumined by the sun appear properly depicted on this paper which should be very thin and seen from behind. And let the said aperture be made in a very thin plate of iron. Let abcde be the said objects illumined by the sun. Let or be the face of the dark habitation in which is the said aperture...nm. Let st be the said paper where the rays of the species of these objects are intersected upside down. Because of their straight lines, a on the right goes to the left at k and e on the left goes to the right at f. And thus it occurs within the pupil.

    On D10v he takes the next logical step, now integrating his drawing of the camera obscura on D8r with his model of the eye with two of its inversions (fig. 1178). On D10r Leonardo had included another modification. Instead of depicting the crystalline lens as a perfect sphere, he had removed a lunule from the posterior section (fig. 1076). This modification is included in his diagram on D10v (fig. 1178). This series of diagrams in the Manuscript D marks his last recorded attempts to explain the inversion of images on the eye. After 1508 he does not return to questions of the visual process.

 

11. Conclusions

    Leonardo's explanation of the visual process had changed dramatically in the period 1490-1508. At the outset he had favoured two possibilities:

1. that only the central ray was oeprative in vision, and
2. that rays coming to the eye converge to a point.

    Each of these alternatives had avoided the embarrassing problem of inverted images in the eye. By 1492, however, his study of camera obscuras and spheres of water led him to explore the possibility that images are inverted twice within the eye.

    In his early versions he posits that a first inversion occurs just behind a pinhole-like pupil and a second inversion in the centre of the crystalline lens which, he assumes, is like a sphere of water. In 1508 he considers yet another possibility: that a first inversion occurs in the crystalline lens and a second inversion occurs in the vitreous body beyond the lens. This explanation he rejects also, and in the end adopts a further alternative wherein a first inversion occurs behind the pupil and a second inversion occurs in the vitreous sphere behind the lens.

    In the meantime the whole nature of his explanation has changed. In 1490 his explanation is largely in philosophical terms and so formulated that it precludes the role of physical images. By 1508, his explanation is in terms of physical models. The visual process is now a domain of physics. Granted his models may remain imperfect. But the challenge is now there to match the models with visual experience and text claims by experiment. The way is prepared for the model eyes of Scheiner in the next century.


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Last Update: July 2, 1999