Dr. Kim H. Veltman

Anatomy and Physiology of the Eye


1. Introduction
2. Vision as the Chief Sense
3. Eyelids and Eyelashes
        3.1 Function
4. Cornea
        4.1 Function
5. Aquaeous Humour
6. Iris
7. Pupil
        7.1 Function
        7.2 Demonstrations of the Pupil
            7.2.i Star through an Aperture
            7.2.ii Candle
            7.2.iii Sudden Exposure to Daylight
            7.2.iv Sudden Exposure to Darkness
            7.2.v Peashooter
        7.3 Theoretical Demonstrations
        7.4 Madrid chapter
        7.5 Comparative Studies of Pupils in Man and Animals
        7.6 Towards Quantification
        7.7 Rules
8. Uvea
        8.1 Function of the Uvea
9. Crystalline Humour
        9.1 Function of the Crystalline Homour
10. Vitreous Humour
11. Retina
12. Orbit
13. Optic Foramen
14. Second or Optic Nerve
        14.2 Function
15. Optic Chiasma
16. Optic Tract
17. Third or Motor Ocnli Nerve
18. Ophthalmic Nerve
19. Ventricles
        19.1 Lateral Ventricle
        19.2 Third Ventricle
            19.2.i Function
        19.3 Fourth Ventricle
20. Visual Power
21. Conclusions

 

 

1. Introduction

    Leonardo considers vision as the most important of the senses and therefore devotes considerable attention to the eye and its properties. From the outset he is explicit in doubting the verbal claims of the Ancients, preferring instead the visual evidence of experiment. On CA119va (1492), for instance, he notes:

Beginning of Perspective

That is of the function of the eye
Now consider, /O/ reader, what we can believe of our ancients, who wanted to define what a thing is soul and life, things /which cannot be/ proved /while/ those things which can be clearly known and proved at any hour have been ignored and falsely believed for so many centuries. The eye experience so clearly as its function.... And yet it has been /described/ innumerable times by countless authors in one way, while I find by experience that it is in another.

    This fresh approach to authority which rejects verbal claims and insists on visual demonstrations helps explain why his notebooks have no lists of tunics of the eye as found in Galen, Witelo, Bacon, Pecham or Mondinus. It also explains why many of the questions he raises concerning vision in a long list on CA360rc (c. 1490) are primarily physical and not philosophical (see Chart 19). Even so Leonardo's approach is not as straightforward as one might at first assume. In his anatomical notes he records his intention to study the eye carefully. Hence on W19037v (K/P 81v, 1489-1510), while outlining the contents of his book he notes: "And then perspective through the function of the eye and of hearing, you would say, of music and describe the other senses." In a note on /ca345vb he writes a reminder: "Write in your anatomy what proportion all the diameters of all the spheres of the eyes have and what distance the crystalline lens has from them." Elsewhere on W12641r (K119/39/r, 1508-1510) he gives even more exact instructions:

In my anatomy of the eye, in order to see well inside without pouring out its humour one should put the entire eye in egg white and have it boiled such that you can cut the egg and the eye transversly in such a way that the half below does not pour out anything.

    Notwithstanding these plans there is no conclusive evidence that he actually made a careful anatomy of the interior of the eyeball. Indeed, his most detailed diagrams of the interior bear striking resemblance to the diagrams of Alhazen, Bacon or Pecham (e. g. fig. 963, cf. figs. 957-962). At the same time, his anatomy of other parts of the visual process such as the orbit, optic chiasma, nerves and ventricles is very painstaking.

    One reason for this discrepancy between such careful studies in some parts and negligence of others is that the visual process in the eyeball only gradually emerged as a problem for him. In the early period he considered both intromission and extromission theories. He also believed that the visual power was situated at a point in the pupil. Questions of image formation were thus not relevant. Gradually he discovered that there was not one point in the pupil to which images converged, but that all points could serve this purpose.

(figure)

Figs. 957-958: Drawings of the eye in Manuscripts of Bacon's Perspectiva.

(figure)

Figs. 959-961: Drawings of the eye in manuscripts of Pecham's Perspectiva communis.

(figure)

Figs. 962-963: Drawings of the eye from Alhazen's treatise and Leonardo's CA337ra.

Questions on CA360rc Answers elsewhere in Notebooks

How and why many things that
are mirrored come to the eye
upside down.

Why a given thing that is
mirrored appears larger than
it is?

Why when a thing is mirrored
it appears smaller?

Which mirror is that which
shows things precisely /the
same size?

Which mirror shows things out-
side itself?

How is the mirror the master
of painters?

Why does the eye go changing
from hour to hour, growing
larger and smaller?

Why does the pupil become
smaller the more light it has
in front of it and, conversely,
grow larger in the dark?

Why are the things seen by the
eye...small and appear large?

Why does a thing seen through
a slit by two eyes become
double and contrary: that is,
the thing seen on the right
side goes to the left eye and
likewise that from the left
goes to the right?

Why does a building int he fog
appear larger?

Why does the eye not see perfectly
except in a straight line?

Why the pyramidal lines which
part from the eye make a
point at the thing seen?

Why the said pyramid, depart-
ing from the eyes and making
a point at a thing positioned
in the water, the lines are
bent on meeting the water and
do not maintain their straight-
ness?

Why the things seen only make
a pyramid in the eye?

How the two eyes make a pyramid
at the thing seen?

Which things the eyes can see
even if only half?

Which things the eyes can never
see half?

Many lines near one another
cannot be numbered and do not
touch line for line.

Cutting a pyramid all things
appear to be small although
they are large.

...things seen are all bent
although they appear.

...cut the pyramid to find
the things.

...eye bent.

...to put in a painting the
things seen.

...which parts from the thing
seen and leads...observes
straight lines when they pass
through two...in the air that
is thick and thin...to know
the size of the sun or some
other planet, because it
cannot be measured between
us.../without the/ action of
the air, that is thick and
thin.

Chart 19. List of Questions raised on CA360rc and his answers elsewhere in the notebooks. The page numbers indicate where they are discussed in these studies.

    Through his studies of the camera obscura he stablished, moreover, that this point was physical and that image formation was also physical. If the pupil acted in the manner of a camera obscura and inverted images within the eye, how was it that images are, nonetheless, seen right side up? Image formation was not a problem of physics. Leonardo began looking for physical conditions to account for a second inversion. He noted that spheres of water inverted the image. The crystalline lens, he reasoned, was like a ball of water. And just as he studied camera obscuras to simulate the pupil, he examined spheres of water to simulate the crystalline lens.

    There remained a flaw in Leonardo's approach. His models of the eye were based not on the structure of the eye itself, but on what logic led him to assume must be the structure of the eye, and this limited the value of his results. More important than these results, however, was the shift in approach that he introduced. The visual process which had traditionally been a purely philosophical problem was now a question of physics, involving model-making.

    Our examination of Leonardo's notes on vision will open with his comments in praise of the eye. His description and anatomy of individual parts will lead to physiology of parts of the eye, for example, how the eyelashes reflect, how the cornea mirrors and refracts, how the uvea reflects and so on. His theories concerning extromission and extromission will then be examined. An analysis of the experiments that led him to abandon his point explanation of vision will follow, and lead to consideration of his theories concerning double inversion of images within the eye. In a subsequent chapter his notes on visual appearances and illusions will be listed and compared with those in Euclid's Optics. A study of his notes on optimal and minimal conditions of vision will complete this section.

 

MODERN TERM LEONARDO'S TERM TIMES             TIMES
                                                                        MENTIONED ILLUSTRATED

eyelid palpebre 15
eyelash coperchio 24
cornea (pupil) luce 70
cornea (pupil (?) cornua 2
pupil (cornea) popil(1)a 253
albuminoid humour/ omore/spera 15
sphere albuginea
crystalline humour/ omore/spera 23
sphere cristallina
vitreous humour/sphere omore/spera vitrea 16
uvea, grape-like tunic uvea 15
visual power virtu visiva 70
potentia visiva 5
imprinting power virtu imprensiva 2
orbit --
optic foramen buso della chassa dell'
occhio
optic chiasma --
optic nerves nervi ottici 21
ventricles ventrichuli
senso commune senso com(m)une 25
imprensiva imprensiva 43
judgment giudizio 5
parte giudiziale 1
virtu giudiziale 1
memory memoria

 

2. Vision as the Chief Sense

    Leonardo considers the eye alternatively as a better sense (CU28, TPL27, 31), a nobler sense (CU31, 29, 40, 28 TPL14, 20, 21, 27, 31, C. 1492; 28, 34, c. 1500 Mad II 62r, 66v, 1503-1504) and as the noblest of the senses (A99v, BN 2038 19v, 1492). The primacy of sight had been emphasized by both Aristotle1 and Cicero.2 Leonardo provides a series of fresh arguments to defend this claim. Some of his arguments are aesthetic. Vision, he claims is the more immediate (CU40, 42; TPL21, 23, 1492) and the more eternal sense (CU40, 42, 12, 39; TPL21, 23, 24, 29, 1492; CU13, TPL16, 1500-1505: W19101r, K/P 197v, c. 1510-1513 or 1515) and associated with divine proportion (CU28, TPL27, 1492), divine proportionality (CU41, TPL32, 1492) and divine harmony (TPL32). Developing ideas also found in Aristotle3 and Cicero,4 Leonardo claims that the eye is a window of the soul.5

    In addition he mentions scientific arguments why vision is the nobler sense and painting the nobler art. The poet, he argues, copies words which are the works of man. The painter copies the visible works of Nature which are the works of God (CU31, TPL14, 1492). Painting goes to the senso commune via the same sense of sight as does the original object: poetry does not (CU23, TPL15; CU40, TPl21; CU42, TPL23, c. 1492; CU17, TPL7, 1500-1505). Painting is more useful and more communicable (CU17, TPL7, 1500-1505). Painting has more conformity with the thing imitated (CU433, TPL411, c. 1492). It imitates with more truth (CU31, TPL14, c. 1492), with more truth and certainty (CU17, TPL7, 1500-1505): with such truth as is possible in Nature (CU41, TPL32, c. 1492) indeed, with the first degree of certainty given its link with mathematics (Mad II 67r, 1503-1505).6 At the conclusion of his imaginary discussion between a poet and a painter on CU34, (TPL28, c. 1500) he launches into a long eulogy of the sense of sight:

Since we have concluded that poetry is in the highest degree of comprehension to the blind and that painting does the same for the deaf, we shall say: painting is worth that much more than poetry to the extent that painting serves the better and more noble sense than does poetry. Which nobility is proved to be treble the nobility of the other senses because it has been chosen to prefer losing hearing, smell and touch /together/ rather than the sense of sight.

    A description of the range of sight follows:

Because he who loses sight loses the vision and the beauty of the universe and remains like one who is locked alive in a sepulchre where he has movement and life. Now do you not see that the eye embraces the beauty of the whole world. It is the head of astronomy. It makes cosmography, it considers and corrects all the human arts, moves man to various parts of the world. This is the beginning of mathematics; its sciences are most certain. This has measured the altitudes and sizes of the stars. This has found the elements and their sites. This has led to the prediction of the future through the course of the stars. This has generated architecture and perspective and divine painting.

Date Passage Term
Coperchio Coperchio di sopra
Coperchio di sotto
1492 1 3 3
1503-1504 Mad II 25v 1
1508 F37r 1
F29v 1
D1v 5 2 2
D2r 1
D9v 2 1 1 (1)
___ ___ ___
10 8 6 24
Palpebra
1508 F30r 2
F29v 4
F29r 3
D1v 5
D4v 1
_____
15

Chart 21. List of Leonardo's terms of eyelids and eyelashes.

 

(figure)

Fig. 964: Modern representation of the eye.

(figure)

Figs. 965-972: Eyelids and eyelashes. Figs. 965-966, W12434; fig. 967, W12435; fig. 968, W12436; figs. 969-970, CA353ra; figs. 971-972, CA301ra.

O most excellent thing above all the other things created by God. What praises are there which can express your nobility. Which people, which languages will be those which can thoroughly describe your true functions.

This is the window of the human body through which the soul mirrors and avails itself of the beauty of the world. Through this the soul contents itself with the human prison and without this the human prison is its torment. And through this, human ingenuity discovered fire, through which the eye acquired once more that which the darkness had at first taken from them.

But what is there that I should carry on in such a long and lofty discourse. What is there that one would not do for it? It moves men from east to west. It has discovered navigation and with this /sense/ man surpasses nature because natural things are finite and the works which the eye commands to the hands are infinite as the painter demonstrates in the fictions of the infinite forms of animals and herbs, plants and sites.

 

3. Eyelids and Eyelashes

    On at least 24 occasions Leonardo uses the term coperchi to refer to both eyelids and eyelashes. He also uses the term palpebre in this double sense at least 15 times. (Chart 21). On rare occasions, such as F30r, he refers specifically to the eyelashes as labri. His rough drawings of eyelashes begin towards the mid-1480's (figs. 965-968, cf. 969-972). Most of his more careful drawings of this part of the eye date from 192 and 1508 when he explores their function.

(figure)

3.1  Function

    For Leonardo eyelashes function as mirrors that reflect images and produce the rays which appear to surround heavenly bodies. Eyelashes thus play a role in his explanation of the optical process and help to account for certain astronomical illusions (see below pp. ). His earliest extant drawings of this reflection at the eyelashes occur on CA141vbc (figs. 982-985, 1490). These are without text. On CA125rb (c. 1490-1492) he again draws reflecting eyelashes (fig. 978) which, as the caption explains, show: " the reason why the rays of the cornea (luce) appear to the eye and why upside down and how the rays are generated in the thickness of the lashes of the eye." On CA125va (fig. 980, c. 1490-1492) he describes an experiment in this connection:

If you take the eyelashes above /the eye/ and draw them downwards with the finger/s/, the stick nm, being dark and bordering on a clear and luminous background, will appear to make a movement contrary to that of the upper eyelashes and this is because distant similitudes, touching the eye at the same level, move by another motion contrary to this.

    He explains how this contrary movement can be connected through a ball of glass corresponding to the sphere within the eye, and the reformulates his:

Experiment how, not moving the cornea (luce) from its site, the objects seen by this appear to move outside their place.

If you regard an object somewhat distant from you, which is lower than the eye and focus your two eyes on it and with one of the hands you open and hold firm the upper eyelashes and with the other you raise the lower eyelashes on high, always holding the pupils (luce) firmly on the object seen you will see this object divide into two, and the one /image/ stands firm /while/ the other moves in a contrary movement to that which you have done with the finger to the lower eyelid.

(figure)

    The opinion of an adversary is now introduced and countered:

How the opinion is false of thsoe who say that this occurs because the pupil (lucec) moves from its position.

If you wish to see how the above mentioned effect does not occur becasue the pupil (luce) moves from its position, look carefully at the eye of one who undertakes a like experiment and consider carefully the space...of the white of the eye which is found between the area above the pupil (luce) and the upper eyelid, and while the viewer moves the lower lid from on high to below, you will never see a movement in the space which is between the pupil and the upper eyelid.

    Two conclusions follows: "Hence the pupil (luce) does not move in its position. How the above-mentioned things show that the pupil inverts that which it sees." Directly beneath the drafts a rough diagram (fig. 977), which he crosses out and redraws (fig. 987) adding a caption: " If you place a finger at abin such a way that the ray made in the eyelash below does not see the pyramid of the rays made by mn, it will be lacking to the eye." He pursues his study of the role of eyelashes on BM115v (1492-1497) in a passage entitled:

(figure)

Of the light which appears in the eye in its friction.

The rays which appear to depart from luminous objects and come to the eye are caused by the eyelashes of these eyes and those below produce the rays above and those above produce those below and if you close one eye and move away the eyelashes in the other you will see this experience.

    The role played by eyelashes is considered at length in both the Manuscript F and the Manuscript D. On F37r (1508) he begins with a general proposition: "Many are the times that the simulacra...of a given luminous /body/ will be two or three times at the same time in a same eye." In the right-hand margin he draws two diagrams (figs. 986-988). These he marks a and b respectively and then explains in the text alongside:

They /i.e. the simulacra/ will be 2 times when...the eye is closed...somewhat, as excessive light causes a viewer to do and with the result that the top lid is somewhat lowered as figure a /shows/. This produces two rays, one percussing in the thickness bathed by ? to the pupil; the other ray goes directly to this pupil.... There will be 3 in figure b: one in the eyelashes above, one in those below and one in the middle of the pupil.

    On F30r this discussion continues (fig. 990):

A luminous body sends three simulacra from itself to the eye, of which one goes directly to the pupil.../and/ the other 2 percuss hitting the convexity of the eyelids and from this there result contrary motions to the opposite lashes of the eye and from these lashes it rebounds in the eye where they are joined below and above with the first simulacrum c, or splendour stamped by the lashes in the form of rays and this the eye does when it is contracted, as he who takes aim at a target.

(figure)

Figs. 989-991 Reflecting eyelashes on CFA208vb, F30r, F29r.

    An explanation of the diagram now follows:

This is proved by displacing the eye m, as wsa said, and you will see two congregations of rays around a luminous body positioned in front. Of which one part goes upwards and the other below and if you interpose a finger between yourself and the luminous body, putting it somewhat below the luminous body and you raise the finger towards the light with a slow motion until you encounter the source of the light below and then you will note that such a luminous body will immediately lose all the rays above and if you make a contrary motion with the finger in between, /the eye and the object/ beginning above the light and with a slow movement lower the finger until it reaches the top of the light then you will see all the rays below lacking...and with this is pro-

    Here the folio ends. The passage continues on F29v opposite:

-ven our proposition because if the luminous body is a and the first ray in the middle, ao, goes directly to the pupil of the eye. The one below, am, percusses on the convexity of the eyelids and more /on the convexity/ of its lashes and produces more simulacra which are created and at once reflected on the brim...n, which constitutes the thickness of the eyelash and from there it rebounds in the pupil (luce) of the eye, with all the images created in the hairs of the eyelids which have a somewhat long shape and are separated and they go with the points upwards, becoming larger towards the extremities as true eyelids do.

Now to conclude our intent, I say that /if you place/ ts...between the origins below...the light and your eye you will out the ray am. Whence by this, the ray will not impress itself in the convexity or curvature of the eyelashes below and for this /reason/ the ray above /which reflects/ at n will be lacking and consequently also in the eye because, lacking the cause of the images, m, /and n/, the effects of the rays m /and/ n will be lacking. Hence it is as defined because in occupying the ray below, the rays above is lost entirely.

    He now introduces the objection of an adversary:

Here the adversary says that to him it appears that such an image comes from the luminous body and passes through the eyelashes and impresses itself in the thickness that the lids of the eyelashes have and from there they bounce to the pupil and this image...is derayed because it is divided by the hairs through which it passes.

Here it is replied that it would, in such an object, occupy the image below and the rays above mn would not be lacking.

    On F29r he provides further evidence against the adversary's proposal:

The same /applies to/ that which is below and this is against the experience proposed i.e. 29v and 28v/ and again one experiments that it is the hairs below which show the rays above to the pupil (luce) by taking a style and moving it slowly acorss the lids below the eye and, in accordance witht he motion that you make to these lids below, you will see made to the rays above and this is a clear sign and an experience born from reason.

    A further demonstration follows:

Again, if you have such rays in the eye and you move the face to the right and to the left on the level, you will see the rays that are born from the lustres turning also and exchanging one another continually.

    He adds detailed instructions concerning procedure:

And this light should stand at least 25 braccia distant from the eye in a dark place and you /should/ experiment slowly and with diligence.

And hold the eye narrow and raise and lower the face such that you see the rays above and below the light at the same time and bracing the head against the wall and holding yourself firm.

    Below this he draws another diagram (fig. 991) showing rays coming from above and being reflected from the lower eyelash to the upper lid and into the eye. A note on the apparent size of distant and nearby objects follows:

The rays of luminous bodies...appear large because no object...which sends its image to the eye...comes closer to the eye than such an object...impressed in the lid of the eye which touches the pupil and from there sends an image to the eye.

    In the right-hand margin he pursues this theme with a diagram (fig. 999) and a further note:

The rays of luminous objects appear shorter when these objects stand closer to the eye, than when they stand further back because when the lids of the eye are half closed, as a person does who wants to see rays around this light and these lids embrace little space above and below this light and since the rays cannot open themselves by more than this space seen by the eye, it is necessary that in such a little space one sees...short rays and that over a long distance one sees long rays, as ab and cd show above.

    He also considers these problems on three folios of Manuscript D. On D1v, he begins with a general heading: "Of the eye" and the subheading: "Why the rays of luminous bodies make themselves larger to the extent that they are more remote from their source." A general proposition follows: "The rays of luminous bodies grow the more they are removed from their sources." This he illustrates with a diagram in the upper right-hand margin (fig. 993, cf. 992) which he then explains in the text proper:

To prove this...let a be the luminous body the image of which impresses itself in the pupil of the eye of this viewer and such impressions, they say, are made in the pupil c. And the same image also impresses itself in the thickness of the upper eyelid b and also in the lower eyelid o. And from both the superior and inferior eyelid the second /and third/ images are reflected to the pupil, c, of the eye. But at the pupil, receiver of the three images, subdivided by the images of the eyelids (which in such a case /are/ narrowed), it appears as if the image of the luminous body, impressed in the thickness of the eyelids are truly subdivided and such divisions are pyramidal because the intervals of the eyelids are also pyramidal. And hence it appears to the pupil, the receiver of these three images, that the images which rebound to it from the eyelids are joined from above and below to the middle image, representative of the luminous body. And it appears to this pupil that the image b is in an and the image o appears to be in am and that both images divide themsleves from the luminous image a.

(figure)

Figs. 992-993: Illustrations of eyelids and refraction on D1v.

    Consideration of attendant circumstances follows:

And since, in closing the lids of the eyelids, it is necessary that the watery fluid, which keeps the eyelids continually moist in the friction of the eye, that this humidity refills the angle generated in the contact which the eyelids make with the eyeball (luce) of the eye and the surface of this watery fluid is concave as is proved in the 4th of the 8th of the waters where it is stated.../that/ the contact which water has with a bank that is wet, is always concave) (and if such a bank were dry then the surface of the water which borders on it will be convex).

Hence finding such an angle created by the contact which an eyelid has with...its eyeball, you will have the surface of the watery fluid filling this angle in a concave figure (and since every concave mirror inside the pyramidal concourse of its rays shows the image of its object upside down, it therefore follows that the weights or lids of the eyes, mirrored in such a concavity along with the image of the light will show these eyelids upside down, and this is the cause why the pupil, being within the concourse of the pyramidal rays of the concave mirror, (why the pupil) sees the radiant pyramids of the intervals of the eyelids upside down.

And this is the true cause of the rays of luminous bodies which dilate more to the extent that it appears that these are clsoer to the eye.

    The folio ends with afterthoughts how the demonstration might be presented more clearly:

    Now a demonstration such as this should be divided into parts to make it better known, placing first its conceptions and other prpositions necessary for a similar proof etc.

    In the right-hand margin of D2r he outlines an experiment to show that rays surrounding bodies are due to an illusion within the eye:

If you wish to certify how the rays of luminous bodies are caused by the images of such bodies which impress themselves in the thickness of the eyelids where they are reflected to the pupil of such eyes, then open the eye to the extent that the pupil does not see these eyelids and you will see the lights without rays.

    This idea he pursues on D9v beginning with a paragraph under the general heading:

Of the eye.

Why the rays of luminous bodies increase together with the space interposed between them and the eye.

The lengths of rays produced by luminous bodies grow together with the growth of the space which interposes itself between those bodies and the eye. Here one needs to define first what the rays of luminous bodies are and whether they have their origin in the eye which observes those bodies or whether they truly originate in such luminous bodies, and concluding that they are born in the eye it is necessary to say why and how etc.

    Leonardo's theory is that the rays which appear to surround stars and other heavenly bodies have their origin in the eye, as becomes clear from the following paragraph headed:

Why luminous bodies show their boundaries filled with straight luminous rays.

The rays that the boundaries of luminous bodies show do not have their origin in those bodies but have their origin in the thickness of the eyelids of the eyes of those regarding these bodies. This is proved first in a persuasive fashion which teaches that an eye which is completely upon will not show such rays around the luminous bodies and if the image of a star or some other light passes to the eye through a minimal aperture made in a /piece of/ paper positioned in front of the eye, these luminous bodies will always be without rays.

    Persuasive argument is followed by reasoned explanation:

But the true proof shows itself by the ninth of the perspective where it is stated (the angle of incidence is always equal to the angle of reflection and hence the rays that appear to extend from the luminous body to the contact of the eye which sees it, originate when the eye, nearly closed, looks through a small aperture made between the lids of the eyes. The image of such a luminous body is mirrored in the thickness of the lids which terminate these eyelids and afterwards this impression is reflected to the pupil of the eye, which pupil takes in three images of a same luminous body, that is, two from the thicknesses of the lids which the eyelids have and one in the pupil...and since...these three images are very close to one another, they appear to the eye to be continuous and joined to the image of the pupil.

    By way of support he uses an experiment also described in the Manuscript F:

(figure)

Figs. 994-998: Eyelids and refraction on D9v.

And the proof which shows the experience and confirmation of our proposal is manifested in the raising and lowering of the face, holding the narrowed eye firmly on the luminous body. This eye, when the face is raised will lose all the rays below this luminous body and this occurs because (the image of this body cannot impress itself in the lower eyelid of such an eye) where the luminous body does not see this, this /body/ cannot impress its image and where the incident ray does not percuss, it does not generate the reflected ray and for this /reason/ the pupil does not take it in.

And the same will occur when the face is lowered because then the thickness of the superior eyelid (of the eye) does not see, nor is it seen by such a luminous body, as a result of which, as was said, the image cannot...impress itself and consequently the eye cannot see that which it does not see, but sees this image in the eyelid below, which eyelid sees and is seen by the luminous body...and thus we have proved our intent, etc.

    The passage ends with the opinion of an adversary:

The adversary says that a ray bends because it goes to the sense from the rare to the dense.

    In the right-hand margin these various reflections of rays are illustrated and further described by captions. Beneath the uppermost diagram (fig. 997) he writes: "This eye sees the ray of the luminous body above." The second diagram shows the opposite situation (fig. 998) as its caption indicates: "This 2nd eye sees the luminous...rays of the luminous body below." The next diagram (fig. 995) considers a further alternative: "This 3rd eye sees...the superior and inferior rays, above and below the luminous rays." Further diagrams, without captions follow (figs. 994, 996). Here he is clearly exploring the limits of the visual field within which reflection from both eyelids is possible.

(chart)

Chart 22. List of Leonardo's uses of the term "luce" (usually cornea).

(chart)

Chart 23. List of Leonardo's use of the term popilla (usually pupil).

(figure)

Figs. 999-1001: Images of objects entering the eye on CA125va , F29r and I35r.

    In Leonardo's interpretation eyelids and eyelashes function as mirrors that produce the rays which appear to surround heavenly bodies and as such account for certain illusions relating to astronomy (see below pp. ).

 

4. Cornea

    Leonardo tends to refer to the cornea as the luce. On CA270rb (c. 1492), for instance, he mentions "the circle of the cornea (luce) which appears in the middle of the white of the eye...." On CA85va (c. 1503-1404) he refers to the luce as "that smaller part of the sphere which is divided by the line st." The accompanying diagram (fig. ) leaves no doubt that the cornea is intended. Even clearer is his description on K119/39/r (1504-1509): "the pupil of the eye is situated in the middle of the cornea (luce), which cornea (luce) stands in the form of a portion of a sphere which, in the middle of its base receives the pupil...." On some occasions diagrams with captions (figs. ) leave no doubt that luce can mean cornea.

    Nonetheless, the term luce, which occurs at least 70 times in the extant notes (Chart 22) remains problematic because it is also used in the sense of "pupil" or "a larger part of the eye." On W19030v (K/P 72v, 1489-1510), for example, he mentions "the luce or the pupil." On CA250va (c. 1490) he refers interchangeably to the space between the pupils (interpopille) and the space between the luce (inter luce) and on A100v (1492) he uses the term "little luce" as if he meant "little pupil." On D3r, by contrast, he refers to the luce as being "the entire sphere labv" (fig. ) which effectively embraces even the crystalline sphere.

(figure)

Figs. 1002-1007: Refraction in the eye. Figs. 1002-1003, W12692r; figs. 1004-1005, BM221v; figs. 1006-1007, BM220r.

(figure)

Figs. 1008-1015: Concerning refraction of the eye. Fig. 1008, CA42vab; figs. 1009-1010, CA222ra; figs. 1011-1012, CA144vb; figs. 1013-1015, W19150r, (K/P 118r).

    On A77 (1492) he uses the term cornua but in such a way that it appears to mean "vitreous humour." He provides no detailed anatomical description of the cornea. Nonetheless, he draws it on various occasions (figs. ) and is interested in the role of the cornea in the refraction and reflection of rays.

 

4.1  Function

    His first extant hints of refraction at the cornea are in two rough sketches on W12692r (figs. 1002-1003, 1487-1493). On W12447v (K/P 33v, 1490-1493) he asks:

Whether images have their proper position in the eye or not?

Whether rays enter the eye /directly/ or whether they are bent at the entrance or not?

    On CA141vb (figs. 1016-1019, 1490), a related sheet, he pursues this theme. Accompanying a first diagram (fig. 1016) he adds the caption: "This eye sees a ray departing from the light and it goes below." Alongside a second diagram (fig. 1017) he writes: "This eye sees the light which is mirrored in b in the middle of 2 rays, one which goes from the cornea (luce) upwards and the other which goes from the cornea (luce) downwards." He then draws a third diagram (fig. 1018) accompanying which he notes:

This sees a ray which parts from the cornea (luce) and goes upwards and
this occurs because that which goes from the rare to the dense...
bends its straightness on entering the dense.

    On CA144vb (figs. 1011-1012, 1490) this refraction at the cornea is again suggested and on CA222ra, cf. figs. 1009-1010, 1492) its necessity is asserted:

(figure)

Figs. 1016-1019: Refraction at the eye on CA141vb.

If the eye looks at the point c in front of if along a straight line it will see the movements made along the line of the ears at a distant position...at the points a and b. Therefore it is necessary that the lines are bent.

    Witelo, in his mediaeval optical treatise had made an implicit comparison between the arrows shot by archers and visual rays.7 On Forst II 69v (c. 1495) Leonardo adopts this comparison to illustrate refraction in the eye: "I also believe that an arrow, /when/ it hits water obliquely, will bend as does a visual ray." Immediately following he describes an experiment relating to this claim:

And you will make a test of this by taking a bow and taking a frame in which a /piece of/ paper is stretched out, which paper is on the water. And having drawn on this paper without moving either the bow or the paper, remove the water and you will discover the arrow and with a thin thread you can see if the centre of the bow and the centre of the aperture made in a /piece/ of paper by the arrow are along the same line or not and in this fashion you will make your general rule.

    He returns to this theme in two sketches on BM221v (figs. 1004-1005, 1500-1505) which he develops on BM220r (figs. 1006-1007, 1500-1505) when he compares the effects of linear perspective and visual perception (see Vol. 1, Part 3.3) and notes: " if the jugment of the eye is inside, the straight lines of the species are bent on its surface, because they go from the rare to the dense." He pursues this question of discrepancy between the size of objects in visual perception and linear perspective on D2r (1508) under the heading:

How the straightness of the concourse of the species is bent on entering the eye.

The straightness of the concourse of the rays made by them at the entrance of the eye is bent and this is why, at an equal distance, the eye sees an object as larger than given by the rules of perspective.

    An example follows (fig. ):

And the reason is that the eye receives on it the intersection of the species ab at op and the perspectivist /painter/ imagining that these rays are straight cuts the rays at r /and/ t and thus finds things produced by his perpsective considerably smaller than they are judged by the eye.

    The objection of an adversary is then raised and dismissed, with the help of his visual ray - arrow analogy:

And if, by an adversary, it were said that the object ab appears larger than it is such that the thing which comes to the eye by the lines alf and bpf appears in space cd seen by the straight /lines/ foc and fpd. This shows itself as being impossible for if you wish to draw an arrow with the power of the lateral rays foc, you would believe (give) you were shooting such /an/ arrow at the site c and you would shoot it at a.

    In the Arabic tradition a device had been developed to measure the amount of refraction in passing from air to water.8 Leonardo adopts this as his own in a diagram on F33v (fig. , 1508). He provides further demonstrations of refraction at the cornea in a series of sketches inw hich he explores the limits of the visual field on I35r (fig. 1001, 1497-1499), I46r (fig. ) CA345vb (fig. , c. 1505-1508); F40r, 34r, (figs. , 1508); D1r, 8r (figs. , ); K/P 115r, 118r (figs. , 1508-1510); K118 /38/r (fig. 1020, 1509-1512); CA42va (fig. 1008, C. 1510) and CA385vc (figs. , c. 1513).

(figure)

Fig. 1020: Cornea on K118 /38/r.

    On D2r (1508) he again broaches the problem of refraction at the cornea asking:

Whether the species of objects are taken by the visual power at the surface of the eye or whether they pass inside.

The glasses of old persons shwo us how the images of objects are fixed on the surfaces of such spectacles and from such surfaces they penetrate bending at the surface of the eye, from which surface it is possible that the eye sees the figures of the said objects. And this is proved to be possible because such a surface is the common boundary between the air and the eye.

    This explanation he develops on D7r (1508) under the heading:

How the pupil receives the images of things placed in front of the eyes only from the cornea and not from the object.

The glasses of spectacles show us how the images of objects stop at the surface of such lenses and then bend to penetrate from this surface to the surface of the eye, from which it is possible for the eye to see the shapes of the aforesaid objects. This is again proven by means of the character of the intrinsic and extrinsic angles made by the rays of the species which penetrate the surface of the eye, that is, the extrinsic angles t and v. And if the pupil were to be flat in itself and penetrated by the rays of the species in such a way that the intrinsic angles would be equal to the extrinsic ones then such angles could not be generated in the pupil of the eye, but as far from the pupil as the centre of the object is from its opposite extremities, i.e., in the intervals from a to f and from a to g which in thepupil would correspond to r to s and r to t. Because if the species were to pass through the flat pupil, together with its surrounding parts and occupy the crystalline humour then the intrinsic and extrinsic angles would necessarily be right angles.

    He is equally interested in the reflection of images from the surface of the cornea. On CA309rb (c. 1490), for instance, he asks:

Why the eye when it sees things on its small surface these appear large to it?

This arises because the pupil is a concave mirror and it is also observed with the example of a ball of glass filled with water, that whatever one puts to the side or in front of it or beyond it appears larger.

    His theory that the eyelids and the surface of the eye function as mirrors, lead him to study the properties of mirrors with respect to vision. Hence on CA125rb (c. 1492), immediately following his discussion of eyelids/eyelashes (see above ) he draws a sketch (fig. 1023) of reversal in a mirror which he then explains:

If the mirror ac takes the thing ab, it will appear inverted to him and likewise cd, and if you raise b on top it will lack its image at the bottom of the mirror at c and thus it happens with the eye that, when the eyelid is raised above, the ray below is lacking.

    On CA141vc (1490-1492) he pursues this comparison between images in a mirror and at the surface of the eye:

No person will see a similitude of another person in the proper place where it refers itself because each object falls on...the mirror at equal angles and if the eye which sees the other in a mirror is not positioned along the line of the species, /then/it will not see it in the place where it falls and if it enters into the lines it will occulude the /image of the/ other person and impose itself on his image.

    A diagram (fig. 1019) in the right-hand margin may have been to illustrate this. In a marginal note he considers a related example (fig. 1027):

If you touch the eye of another person on the mirror, it appears to the other /person/ that he touches yours.

Let no be the mirror, let b be the eye of your friend, let d be your eye. The eye of your friend appears to you at a and to the friend it appears that yours is at c and the intersection of the lines is made at m and whoever touches m will touch the open eye of the other person.

    This theme of images mirrored in the eye of another person is continued on A37v (1492), but now in another context, namely, to help visualize the apex of the visual pyramid which he believes ends in a point within the eye (- an opinion he will later reject):

As regards the point which comes to the eye it is understood with greater facility, for if you look into the eye of someone you will see there your similitude. Whence if you imagine 2 lines departing from your ears and meeting at the ears of the image of yourself which see in the other eye, you will recognize clearly that there lines are restricted in such a ways that, going on a little beyond your image mirrored in that eye /these lines/ would touch at a point.

(figure)

Figs. 1021-1022: Demonstrations concerning cornea on F31v.

    Well over a decade later he returns to these analogies between the surface of a mirror and the surface of the eye. On CA190vb (1505-1508) he draws a reversal diagram (fig. 1024) beneath which he notes that "the image of the real object changes the right side to the left and the left to the right at the surfaces of mirrors." Lower down, he draws the same reversal principle in connection with a curved surface (fig. 1025), which presumably represents the eye. To the left of this he compares the reversal principle in mirrors with that of camera obscuras.

The image of objects are of two natures, one of which receives the true images of the real object; a 2nd...retains the same, but with confused boundaries of their shapes and the first passes with parallel lines within the surface of plane mirrors and the second passes through the (narrow) apertures of thin walls in a dark place into which it enters.

    On F31v (1508) he returns to the question raised on CA141vc, concerning where one sees images mirrored on the surface of the eye (fig. 1022):

The sense does not see an image of an object in the same position on the surface of the eye as does the eye of a viewer of this image.

The sense b sees the image of an object a at position d and the eye of another viewer of this image positioned at esees the same image in another place, that is, at site c, as is proved by the 7th of the 2nd.

    In the early period he had drawn an object ab in front of a mirror cd on CA125rb (fig. 1023) to explain the mirroring process of the cornea. On D4r (1508) he redraws this diagram in the margin using the same lettering, (fig. 1026). The elongation of the later figure appears to be accidental. Beneath it he writes a corrective notes: "This figure ought to be square." Alongside the diagram he explains:

Why a mirror changes the sides of an image from right to left and from left to right.

The image of every object changes in the mirror with its right side facing the left of the mirrored object and similarly the left /facing/ the right. This is proved to be of necessity because every natural action is made by Nature in the shortest way and time possible.

    A specific case (fig. 1026) is now considered:

Let ab be a face which sends its image to the mirror cd and this face will have another face in the mirror facing it which will have its left eye c facing the right one and similarly the right eye d will be facing the left eye b.

    He next introduces an adversary's opinion which he then dismisses:

And if it were stated by the adversary that the right eye of the adversary...were facing the right of the object, /then/ I would produce the lines from the right of the image to the right of the object and likewise from left to left, which lines are ad and cd, which are seen intersected, and it is proven that in all intersected lines the right extremity of the one...will /go/ to the opposite extremity of the left side of the other and such an effect is not made by the shortest line because the diameter of a square is always longer than its side and here ab is the diameter of a square abcd of which ac is one of the sides /such/ that in this way is concluded that which is necessasry for the proof of such an affect.

    At the end of the passage this mirroring effect is compared to what occurs when one looks into the eyes of others:

And such an effect in the mirror is like one who looks at you with a left eye facing your right eye which, by a miracle, makes itself from left to right, as do the letters that are stamped in the wax in the cornelian.

    These questions of images mirrored at the cornea help explain his interest in the correspondence between the original arrangement of objects and their arrangement at or in the cornea. On F31v (1508), for instance, he notes:

The spaces...between the images of the stars on the surface of the eye have the same proportion as the spaces which the stars in the sky have interposed between them.

Even though the images of the stars are all in all the surface of the eye and all in every part of this, and even though each image is superimposed on each of the other images, as appears to another eye which looks at it as at the surface of another mirror, it is nonetheless true that as far as the inside of the pupil is concerned, whenever the coming of an image of a star from the outside is occluded, this image will not proceed to impress itself on another part of the eye but will remain without impression in this eye because the site to which it is directed is impeded by the said occulusion.

    This he illustrates with a cursory marginal sketch (fig. 1021), in which he draws the eye as a half-moon. Above this he draws two stars as half circles. The star on the left sends its rays to the eye. The rays of the star on the right, impeded by a rectangular object, do not reach the eye. On D2r (1508) he pursues this problem under the headings:

Of the eye
Whether the idola or image has a fixed position on the eye or not.
The images of immobile objects have fixed positions on immobile eyes.

    To demonstrate this he draws a diagram (fig. 1028) which he explains in the text alongside:

Let the object be ab /sic: a1o1/ which,...by the 7th /proposition/, sends its raysat a/-1a/ by the shortest possible way to the pupil a o and the opposite extremity of the object oo/1/ does the same. Hence the image of the extremity a/1/ does not impress itself at itself at the site o of the pupil, nor does o/1/ impress itself at a.

    He now poses the question anew:

Whether objects send their images to the eye with the mmbers proportioned as they are in themselves.

Objects do not send images to the eye...with the parts proportioned as they are in this object. This is proved by the ninth and how, among objects of equal size, the more remote shows itself as smaller.

    In the margin he draws two diagrams (figs. 1029-1030) the lower of which he describes in the text that follows.

Hence let a be the eye and let its object be bcd. By the said 9th, I state that the parts d /and/ b of this object will show themselves as smaller than the part c because they are more remote from the eye than c as is proved by the definition of the circle /of which/ acnm is a sector and bd exceeds the distance that there is from the periphery of the sector to the said eye.

    He pursues this question of the proportions of images at the eye on D10r under the heading:

On the proportions which the positions of the images have which are impressed on the eye.

The proportion which the positions of objects spread throughout the countryside opposite the eye have, is never identical to the proportion (of) of these images spread out over this eye if these objects are not equidistant from the curvature of the eye.

    He now draws a "1st" illustration which he describes in the text that follows:

This is proved. And let the surface of the eye be ae/g/c and let the objects spread throughout the countryside opposite be desrf. I state that t, e, s /and/ f, being objects /which are/ equidistant from the surface of the eye, will be sown on this surface of the eye in the same proportion as they are sown in this landscape (m) and this is proved by the 9th of this which states /similar triangles, equally cut, with an intersection equidistant from their bases have sections in the same proportion amongst themselves as (are) the bases of these triangles have amongst themselves.

But if intersections are not equidistant from their bases then the sections will not observe the same proportion as that of these bases. It follows that the triangle her, because its intersection og is not equidistant from the base er, that the section og is not in the same proportion to er as the intersection an (made at the same distance from the angle h) to the base of triangle de which is half the base er.

(figure)

Figs. 1028-1031: Concerning images entering the eye. Figs. 1028-1031, D2r; fig. 1032, CA141vb.

    On D10r he pursues this question:

Of the proportions which the positions of the images have which are impressed on the eye.

The proportion which the positions of objects spread throughout the countryside opposite the eye have, is never identical to the proportion...of these images spread out over this eye if these objects are not equidistant from the curvature of the eye.

    A "1st" illustration (fig. 1034) and description follow:

This is proved. And let the surface of the eye be ae/g/c and let the objects spread throughout the countryside opposite be desrf. I state that t, e, s /and/ f, being objects equidistant from the surface of the eye, will be sown on this surface of the eye in the same proportion as they are sown in this landscape...and this is proved by the 9th of this which states (similar triangles, equally cut, with an intersection equidistant from their bases have sections in the same proportions amongst themselves as...the bases of these triangles have amongst themselves.

    He goes on to describe a second case (fig. 1033, cf. 1035):

But if intersections are not equidistant from their bases then the sections will not observe the same proportion as that of these bases. It follows that the triangle (her, because its intersections og is not equidistant from the base er, that the section og is not in the same proportion to er as the intersection an (made at the same distance from the angle h) to the base of its triangle de which is half the base er.

(figure)

Figs. 1032-1034: Images at the surface of the eye. Figs. 1033-1034, D10r; fig. 1035, CA141vb.

    On E15v (1513-1514) he returns once more to this theme:

When we look at the...sky full of stars without looking at one star more than another then the sky is seen seeded with stars and they are proportioned in the eye as in the sky and thus their spaces are similar.

 

5. Aqueous Humour

    In the early period Leonardo has no specific term for the acqueous humour. On CA270rb (c. 1490), for instance, he refers to it simply as "that water which is in the cornea" (luce). On D2r (1508) he refers to the aqueous humour as the albugineous humour - albeit this term can also mean vitreous humour. In the extant notes there is no record of his studying either the properties or the functions of this humour.

 

6. Iris

    He has no specific term for the iris although he draws it clearly on at least three occasions (see title page to part three).

 

7. Pupil

    Leonardo's term for the pupil tends to be popil(1)a which he uses at least 253 times in the extant notes, (Chart 23). His use of the term is complex, however. On CA309rb (c. 1480), for instance, he describes it as "a concave mirror." On D1r (1508), when he refers to "why Nature made the popilla convex, that is, elevated as part of a ball," popilla appears to mean "cornea" and could even mean "eye." His alternative term for pupil is luce9, which is no less complex, luce tends to mean cornea (see above p. ) and can be synonymous with eye (eg. F32r). Hence the terms popilla and luce are both ambiguous and have a range of meanigns including pupil, cornea, and eye.10

 

7.1  Function

    In some early notes he describes the pupil as if it were merely an aperture directly linked with the optic nerves (eg. A77, BM171v, fig. ). In other notes (eg. CA125rb), he explores the analogy between pupil and camera obscura, which leads him, on the one hand, to study camera obscuras with apertures of various shapes (see above p. ) and, on the other hand, pupils of various kinds, round, slit-like, etc. (e.g. CA262rd, Mad II2 25r, G44v). In the early period he is interested in pupil size because it provides him with an explanation why distant objects are seen unclearly, as on A100v (BN 2038 20v, 1492) where he analyses:

Why faces in the distance appear dark.

We see clearly that all the images of evident things that there are from objects large as well as small, enter the sense by the little pupil (luce) of the eye. If the images of the size of heaven and of earth pass through such a small entrance, amongst such things, the face of a man being practically nothing through the distance which diminishes it, occupies so little of this pupil that it remains incomprehensible and having to pass from the surface to the imprensiva through a dark medium, that is, the hollow nerve which appears dark. Another reason cannot be alleged in any other way: if this point is black which stands in the pupil, and since it is filled with a transparent humour like that of the air, and has the function of an aperture made in a board and looking at it, it appears black and the things seen through the clear and obscure air are confused in darkness.

    As his studies progress he becomes convinced that there is a direct connection between pupil size and the apparent size of objects. To confirm this he describes no less than five practical and two theoretical demonstrations, some of which recur in an extended passage on pupils on Mad II 25r-27r. He also examines differences between pupils by day and at night and makes comparative studies of pupils in human beings, owls, cats and lions. He refers to the pupils of various owls (common, horned or long-eared, tawny, barn and little), panthers, leopards, wolves, lynxes and Spanish cats. On several occasions he compares the relative size of pupils with the sizes of the imprensiva.

    Each of these aspects of his pupil studies will be considered in turn. In a later section it will be shown that he has an ulterior motive for being so interested in this connection between pupil size and apparent size: it has fundamental consequences for his studies of astronomy (see below pp. ). This helps explain why Leonardo writes more about the pupil than any other part of the eye.

 

7.2  Demonstrations of the Pupil

    In order to confirm that changes in pupil size determine apparent size Leonardo devises five practical experiments involving:

1. looking at a star through an aperture;
2. looking at a candle;
3. sudden exposure to daylight;
4. sudden exposure to darkness, and
5. looking through a peashooter.

    In addition he describes two theoretical demonstrations. Each of these will be discussed in turn.

(figure)

Figs. 1036-1037: Images entering the pupil on F36v.

Why a thing seems larger when seen by a larger pupil.

That thing will appear greater in light and in size which will be seen by a larger pupil. This can be experimented with our eyes,...if you make an...aperture as small as can be in a piece of paper and bring it as close to the eye as possible and you look at a star through this. Which /eye/ can only function with the little part of the pupil which sees this star with much space of the sky around it, /and/ it sees it as so small that hardly anything can be smaller and if you make such an aperture close to the extremity of the paper you will at the same time be able to see the same star with the other eye and it will appear large to you and thus in the said time you will see with two eyes a /single/ star 2 times of which the one is minimal and the other is large. You can also see the entire body of the sun and with little brightness because to the extent /that/ its magnitude diminishes to that extent does its brightness diminish as was proposed above. And from this it arises that great lights see little of the ray because excessive lights impede the sight.

    In the Manuscript F he uses this experiment to develop his claims concerning pupil size. On F36v (fig. 1036), for instance, he draws a light source at m passing through an aperture op in a sheet of paper ac to the eye at n. Alongside he explains:

If some luminous body be seen through a minimal aperture made in a /sheet of/ paper...brought as close to the eye as possible, the luminous body..., even if it be seen entirely, will appear that much smaller than usual by the extent to which this aperture is of a smaller quantity.

(figure)

Figs. 1038-1040: Demonstrations concerning pupils. Figs. 1038-1039,

F33r; fig. 1040, F32v.

 

7.2.i  Star through an Aperture

    On C6v (1490-1491) he describes how a candle 400 braccia from the eye appears much larger than it is until a small stick is placed in front of it (see below p. ). This experience he develops on A64v (1492) into a:

Test to see the true size of luminous bodies.

If you wish to see the true size of these luminous bodies, take a thin board and make an aperture the size of a small point of lace and place it as close to the eye as you can in such a way that, looking at the aforementioned light through this aperture, you see enough space of air around it and thus removing and /re/placing this board from and to your eye quickly you will see this light grow and diminish quickly.

    He returns to this demonstration on CA351vb (c. 1495-1497?) under the heading:

Of the eye and light.

If you look at a luminous body in the far distance through a small aperture, it will appear to you to diminish and if you look at it from close by, it will not make it alter at all, that is, if you look at this light one or two braccia away from the named aperture, and it will not make a change /in this case either/ looking through this aperture or outside it.

    In the above demonstrations connections between size of aperture, pupil and apparent size remain implicit. On D5r (1508) he makes these connections explicit in a passage with the marginal heading: "This occurs because /a/ lesser power has less potential power than /a/ greater...and through this coming..." Here his train of thought breaks off, but on F33r he pursues the problem (see above p. ) beginning with a diagram (fig. 1039) which is a:

Demonstration how the percussion of solar rays penetrating through apertures are more luminous in the centre than from the sides and the reason for this effect.

In the centre, m is the most luminous because here it sees the entire body of the sun as the lines mf and mg show which touch the sides a and b of the aperture. And or sees half the sun and cd sees no part of the sun. Hence it is very dark.

    In the lower margin he redraws the diagram (fig. 1038) and in the text opposite he continues his explanation:

Now let us say that ab is the minimal aperture that I have made in the paper through which I look at a star or some other luminous source and that cd is my pupil. Now in order to observe this star through the aperture ab, its /the star's/ image descends in its entirety to m and is small and if this aperture were not interposed between the eye and the star, I would see the whole star with the entire pupil cd as at first and it appears larger to me because I see it with a greater power because, in such a view the entire pupil will be brought into use as is seen by the 2 lines fc /and/ gd.

    This amounts to a geometrical demonstration of his claim that the size of the pupil's aperture determines apparent size.

(figure)

Figs. 1041-1044: Further demonstrations concerning images entering a pupil. Figs. 1041-1043, F32v; fig. 1044, F32r.

    On F32v, the folio opposite, he redraws this diagram (fig. 1040 cf. figs. 1038-1039) and sums up his claim in a marginal note:

The entire pupil of the eye which, with each of these circles from the greatest to the least...diminishing infinitely, can see the entire body of this star but will see it as smaller to the extent that it sees it with a smaller portion of the pupil (luce).

    Not content with this demonstration involving one star, he drafts a sketch in the lower right margin (fig. 1043) involving three stars. This he redraws at the top centre (fig. 1041) beneath which he asks:

Why in looking at...the sky one sees various stars with great brightness...and looking at them through a minimal aperture in a small /sheet of/ paper placed in contact with the eye you again see the same amount of stars but diminished /in size/.

    His answer follows:

This is defined with the nearby positioned figure above. Let us, therefore, say that the size of the pupil is all the greater circle kl into which come the impressions from the 3 stars a, b /and c. I say that the eye or the pupil (luce) kl receives them through the lines dkel, fkgl and hkil. But if this eye cannot use more than the part nm as a result of having to look at such stars through the aperture in the /sheet of/ paper, /then/ even in the part nm it will see the images of these 3 stars but they will be seen as smaller to the extent that nm is smaller than kl and these 3 stars will be seen by the 6 lines dnem, fngm and hnim.

    The accompanying diagram (fig. 1041) appears to show the three stars superimposed on one another. Aware of this ambiguity he drafts a further diagram (fig. 1042) in the upper left-hand corner, with the caption: "the images are not sueprimposed one upon the other." This he restates at the top of F32r: "The images of opaque bodies are not superimposeed upon one another, the eye that judges them remaining without motion." In the margin beneath this he redraws the diagram drafted on the verso (fig. 1044, cf. figs. 10421-1043) and explains: "In the same mirror or pupil...is the image of all objects positioned in front of it and each of these objects is all in all the surface of the mirror and all in each minimal part of this." This "all in all" demonstration, (see above p. ) reduces the problem of image formation in the eye to a physical model which can be analysed with geometrical principles. He adds how this can be tested experimentally:

This is experimented with the motion of the eye which will see the moon with all the stars in this mirror...and imprints itself on its surface and if you then move a little with the eye it can imprint itself elsewhere on such a mirror and many will see one imprinted upon the other and...you could do this likewise innumerable times.

    Having compared the pupil with an aperture in a sheet of paper and with a mirror, he now suggests that one can use an aperture in a sheet of paper combined with a mirror to simulate effects in the eye: tracing out the size of stars on the mirror and then, by moving both aperture and mirror, simulate the effects of the eye's motion, each time tracing anew the configuration of the stars seen. He is not content with his diagram, however, and therefore redraws it (fig. 1045) with the caption "this figure is better than the other." In the main body of the text, a full explanation follows:

(figure)

Figs. 1045-1048: Demonstrations concerning images entering the pupil. Fig. 1045, F32v; fig. 1046, F28r; fig. 1047, F32v; fig. 1048, F28r.

...with the entire pupil (luce) of the eye ab I see the entire heaven/s/ ef with 3 stars within nmo even though many other stars of the heavens could be seen as is shown by the two lines at /and/ bs. But these do not concern our discussion. Hence I say that the portion ef of the sky is seen by the entire pupil ab and if one sees such heavens through the...small aperture of the perforated paper it will send its image with the three stars to the part cd of the eye and it will appear that much less to the extent that cd is less than ab.

    He is still not satisfied. On F28r he writes: "it is proved here that the visual power is spread throughout the entire pupil of the eye." In the margin he again draws three stars surrounded by a circle pq (fig. 1046), the images of which pass through an aperture ord onto the pupil abcnmo. Below this he develops a diagram he had drawn previously on F33r (fig. 1048, cf. fig. 1039). At the bottom, a further draft (fig. 1047). None of these are explained, however. On TPL628 (1508-1510) he uses his aperture demonstration to explain why the moon appears dull by day and bright by night. His first reason is that colours are better seen when they are in greater contrast to one another (see below pp. ) and then adds:

the second /reason/ is that the pupil is larger by night than by day as has been shown and a larger pupil sees a luminous body with greater quantity and more excellent brightness than the lesser pupil as is shown by him who looks at the stars through a little aperture made in a /piece of/ paper.

    On TP477b he mentions the experiment again:

(figure)

Figs. 1049-1050: Experiments concerning pupil size on I19v and L14r.

Precept

The eye which will have a larger pupil will see objects as having a larger size.

This is shown in looking at a celestial body through a small aperture made with a needle in a /piece of/ paper which, not being able to act on more than small part of this cornea (luce), this body appears to diminish by so much of its size as the part of cornea (luce) which sees it is less than the whole.

 

7.2.ii  Candle

    His second demonstration of the link between pupil size and apparent size begins with a general statement at I19v (1497):

Experiment of the increase and diminution of the pupil with the motion of the sun or some other luminous body.

(When the sky is darker the stars will show themselves as larger) and if you illumine the medium these stars will show themselves as smaller and such an alteration originates only from the pupil which increases and diminishes depending on the brightness of the medium which is found between the eye and the luminous body.

    A specific experiment follows (fig. 1049):

Let an experiment be made with a candle placed over the hand at the same time as you look at a given star. Then lower this candle little by little until it is close to the line which comes from the star to the eye and then you will see the star diminish so much that you will practically lose sight of it.

    On I20r, the folio opposite, he pursues the theme: "The pupil of the eye standing in the air, in every degree of motion made by the sun changes degrees of magnitude," and its converse: "And in every degree of magnitude /of the pupil/ the objects /which are/ seen change to different sizes." Not content, he crosses this out and reformulates it:

And in every degree of magnitude...a same thing /which is/ seen will show itself of different sizes although of ten the comparison of surrounding things will not allow one to discern such alteration of a single object at which one looks.

    A decade later he develops these ideas further on D5v (1508):

The pupil of the eye will change to as many sizes as are the varieties of brightness and darkness of the objects which are represented in front of it.

In this case Nature has made provision for the visual power, when it is offended by excessive light to contract the pupil of the eye and when it is offended by various darknesses to increase this pupil (luce) like the mouth of a purse. And here Nature acts like one who has too much light in his home, who half closes a window or more, or less, depending on necessity and when night comes he opens the window entirely in order to see better the light within his house. And here Nature uses a continuous equation with a continuous tempering and equalizing...with the increase of the pupil...or its diminution in proportion to the aforementioned darkness or brightness which continuously represent themselves in front of it /the pupil/. And you will see this experience in animals...of the night such as cats, long-eared owls, tawny owls and the like which have the pupil small at midday and very large at night. And all the terrestial animals of air and water do the same but the nocturnal animals /do so/ to a greater extent beyond comparison.

    At this point he describes his candle experiment:

And if you wish to experiment with a man hold the pupil of the eye fixed, holding a lighted candle somewhat removed and have it /this pupil/ look at this light as you gradually bring it closer /to the pupil/ and you will see that the closer this light approaches, the more it diminishes.

    He summarizes these ideas in two marginal ntoes:

On the expansion and contraction of the pupil of the eye from day to night and more in nocturnal animals than in others of the day.

On the eyes of nocturnal animals the pupils of which expand greatly more at night beyond comparison with those /animals/ of the day.

 

7.2.iii.  Sudden Exposure to Daylight

    On C16r (1490-1491) this candle experiment recurs in connection with the problem of the eye's sudden exposure to light.

On the eye.

The eye /which is/ used to the darkness, which suddenly sees the light is hurt, whence it immediately choses itself, being unable to endure this light. And this occurs because the pupil, wishing to recognize any object in the accustomed darknesses increases in size, using all its force /in order/ to send to the imprensiva the image of the umbrous bodies. And the light suddenly entering within, has the effect that too great a quantity of the pupil, previously in darkness, is hurt by the oncoming brightness, directly contrary to the darkness to which the eye was accustomed and habituated and these /darknesses/ seek to maintain their being there and not without detriment to the eye they part from their site.

Again it could be said that the pain which the eye /in/ darkness receives through the sudden light occurs through the sudden contraction of the pupil which is not without the sudden contact and friction with the sensitive parts of the eye.

And if you wish to see an experience of this, observe and consider wellt he size of the pupil of one who is looking at a dark place and then have a candle placed inf ront of it which is quickly brought nearer the eye and you will immediately see a diminution of its pupil.

    On CA125vb (c. 1490-1492) he again drafts a note how the eye is hurt when suddenly exposed to an intense light, and adds:

...if you wish to see the experience, arrange that a nocturnal animal has the sun on only one of its eyes and you will see how much less is the pupil in the eye seen by the sun than in the one which does not see it.

    This he crosses out and on CA125ra (c. 1490-1492) takes up the theme again:

I find by experience that the blackness or near blackness, the rough and raw colour that appears within the pupil does not serve any other function than to increase or decrease the size of this pupil: to increase /it/ when the eye looks at a dark place; to decrease /it/ in looking at the light or at a luminous object.

    On H88 /40/r (1494) he cites both the case of sudden exposure to light and the experiment with an aperture:

That pupil will be larger which will see the things of larger shape.

This is shown in seeing luminous bodies and maximally celestial ones when the eye emerges from the darkness and suddenly looks at these bodies. They appear larger and then they diminish and if you look at these bodies through a little aperture you will see them smaller because a smaller part of this /pupil/ will be adopted in this operation.

    He restates these ideas in the form of brief precepts on H91/43/v (1494):

That eye which emerges from the shadows will suddenly see a luminous body which will appear considerably larger to it at the first glance than in continuing to look.

    The luminous body will appear larger and more luminous to two eyes than to one.

That luminous body will show itself of a smaller size, which is seen by the eye through a smaller aperture.
That luminous body of a long shape will show itself as rounder as it is further from the eye.

    On W19030v (K/P 72v, 1489-1510) he again cites both the demonstration of bringing a light closer to the eye and the sudden exposure of an eye to daylight (see below p. ): "that part of the black appears darker which is closer to the white and likewise /that part/ will appear less dark which is further from this white." On CU459 (TPL491, c. 1492) he expresses this idea as a rule:

Precept C

Among things equally dark and equally distant, that object will show itself to be darker, which borders on a whiter background.

    On CA397rb (1497-1499) he begins to formulate a note: "Who looks at the black object on a white background" and then stops short. In the period 1505-1510 he considers these questions afresh on CU151 (TPL204) headed:

On the colours which are shown to vary from their essence through the comparison of their backgrounds.

No boundary of uniform colour will show itself to be equal if it does not terminate in a background of a colour similar to itself.

This is seen manifestly when black terminates with white and white with black, each colour appears more noble in the confines of its contrary than it does at its centre.

    He considers this intensifying effect of contrasting colours again on CU154 (TPL231):

On the nature of the colours of backgrounds on which white borders.

A white object will show itself /as/ whiter which is seen against a darker background and will show itself darker which is in a whiter background and this the gleaming (fioccare) of snow has taught. When we see it against the background of the air it appears dark and when we see it against a background of some open window, through which one sees the darkness of the shadow of this house, then this snow iwll show itself as very white.

    On CU184 (TPL238c, 1505-1510) he gives another example of the effects of contrasting colours in a passage entitled:

On the nature of comparisons

Black vestments make the skin of human faces appear whiter than they are and white vestments make the skin appear dark and yellow vestments make them appear coloured and red vestments show them pale.

    He therefore urges that contrasting backgrounds are more appropriate, as on CU148 (TPL229, 1505-1510):

Of the backgrounds that are more appropriate for shadows and lights.

Among backgrounds that are appropriate for illuminated or shaded boundaries of any colour, those will be more distinct from one another which are more varied, that is, that a dark colour should not terminate in another dark colour, but one that is very different, that is, white or participating of white and similarly a white colour should never terminate on a white background, but, as far as possible, in a dark /background/ or /one/ partaking of dark.

    While he generally recommends that white should always border on dark and conversely, on CU150 (TPL230, 1505-1510) he considers a situation where this is not the case:

How one should act when white terminates on white or dark on dark.

When the colour of a white object comes to terminate in a white object, then the whites will either the white or not and if they are equal then that which is closer will become somewhat dark/er/ at the boundary which it makes with this white and if this background is less white than the colour that borders in it then the bordering colour will stand out of itself from the /colour/ different from it without other help from a dark background.

    On TPL206 (1505-1510) he suggests that a colour seen against a background of the same colour appears more beautiful:

What part of a same colour will show itself as more beautiful in /a/ painting

Here one wishes to note what part of a same colour will show itself as more beautiful in Nature, whether it is that which has lustre or that which has the light or that of the middling shade or that which is dark or indeed that which is transparent.

Here one must determine which colour it is of which it is asked, because different colours have their beauty in different parts of themselves. And this shows that black has its beauty in the shadows and white in the light and azure and green and tan in the middling shade and yellow and red in the light and gold in reflection and lacquer in the middling shadow.

    This idea he restates on TPl217c (1505-1510):

What part of the surface of bodies will show itself of a more beautiful colour?

The surface of that opaque body will show itself of a more perfect colour, which can have as a near object a colour similar to it.

    Meanwhile, his experiments with camera obscuras had made him aware that the usual rules of contrast do not always hold. On CA195va (1508-1510) for example, he explains:

Why black bordering on white does not show itself as blacker than where it borders on black, nor does white show itself as whiter in bordering on black than on white, as do the species which pass through an aperture or the boundary of some obstacle.

    Nonetheless such cases remain the exception and he continues to favour situations where contrasting colours are positioned opposite one another. On CU183 (TPL190a, 1505-1510), for instance, he expresses this in terms of a rule:

Now note that if you wish to make an excellent darkness make it through a comparison with an excellent whiteness and likewise you make an excellent whiteness with maximal darkness and a pale colour will make red appear a more fiery rose and this rule will be more distinct in its proper place.

    A second rule follows:

There remains a second rule which does not try to make the colours in themselves of the most supreme beauty that they naturally are, but that company /of another colour/ renders grateful the one and the other, as does green to red and red to green such that the one renders the other graceful reciprocally as does green with blue and here is a second rule, generating from ungraceful company, as blue with yellow which whitens or with white and the like which will be discussed in their /proper/ place.

    He restates these precepts on CU145 (TPL232, 1505-1510):

On the boundaries of objects

Among objects of equal brightness that will show itself of lesser brightness which will be seen in a background of greater brightness and that will appear whiter which borders on a space which is darker.

And the skin will appear paler in a red background and the pale /colour/ will appear reddish, being seen in a yellow background and similarly the colours will be judged to be what they are on the basis of the backgrounds which surround them.

    On CU153 (TPL252, 1508-1510), he returns to these ideas:

Backgrounds

On the backgrounds of figures, that is, the bright in the dark and the dark in the white background.

Of white with black or black with white, the one appears more powerful through the other and likewise the contrary, the one always shows itself more powerful.

    He reformulates this on CU751 (TPL769, 1508-1510):

Why the boundaries of opaque bodies sometimes show themselves as brighter or darker than they are.

The boundaries of shaded bodies show themselves /as/ brighter or darker than they are to the point that the background which surrounds them is darker or brighter than the colour of that body which borders on them.

    In the late period he returns to this theme on CA184vc (1516-1517) in a passage entitled:

Of colours

Of colours of equal brightness that will show itself brighter which is of a darker background. And black will show itself as darker than it is in a background of greater brightness.

And red will show itself more fiery than it is in a background that is more yellow and thus will do all the colours surrounded by their directly contrary colours.

    Other passages concerning this theme have been cited elsewhere (see vol. one, part three.1).

 

7.2.iv.  Sudden Exposure to Darkness

    In addition he considers a converse demonstration, namely, when the eye suddenly leaves the daylight in order to enter an enclosed space, as, for example, on Forst II, 2 158v (c. 1495) under the heading:

Of perspective.

The eye, which departs from the white illuminated by the sun and goes into a place of less light, everything appears tenebrous to it. And this occurs because the eye which stands in this illuminated white /daylight/ contracts its pupils in such a way that if they were at first a /given/ visual quantity, they would lack more than 3/4 of their quantity and lacking quantity, they lack power.

    At this point he introduces and answers a potential objection:

Although you could say to me: a little bird would see much less and through his small pupils the white would appear black. From this side I would reply to you that here one attends to the proportion of that part of the brain devoted to the visual power and not to some other thing.

    This objection answered, he continues with his train of thought:

Or to turn: this our pupil expands and contracts depending on the brightness or darkness of its object and because it makes this expansion and contraction over a certain time, it does not see at once when it departs from the light and goes into the darkness and likewise /when it goes/ from the darkness to the light. And this thing has already deceived me when depicting an eye and /it was/ from this that I learned it.

    On L41v (1497, 1502-1503) he describes how a person sees a dark place from the outside (see below p. ):

On Painting.

The eye that stands in the luminous air and looks at a dark place, this site iwll show itself of much greater darkness than it is.

This occurs only because the eye that stands in the air diminishes its pupil the more that the air which is mirrored there is more luminous and to the extent that this pupil diminishes more, the less luminous will the thing seen by it show itself.

    He then mentions what happens when this person enters a dark place:

But when the eye enters some umbrous place the darkness of this umbrous place at once appears to diminish.

This occurs because the more the pupil (luce) enters into dark air, the more its size grows, which growth has the result that the great darkness appears to diminish.

    He develops this description of a person entering a dark place on Mad II 70v (1503-1505), opening with a general statement and a question:

The pupil of the eye expands and contracts with slowness in seeing dark or luminous things.

Why does the eye positioned in a luminous place see darkness within each house where, /when/ the eye is later inside, it appears to be fairly luminous?

    To which he replies:

That which is asked originates because the pupil, being positioned in the luminous air, being offended by excess light, withdraws and diminishes its quantity in such a way that it can support the brightness of the air, which brightness diminishes to the eye along with the diminution of the said pupil.

And from this it follows that looking with this disposition of eye at the aforesaid houses, these appear to it to be dark because, if the strongly luminous air produces little light, the things which are illuminated by the air will come to show themselves as dark to such an eye.

    He returns to this demonstration once more on D7v (1508):

Every enclosed space appears darker in seeing it from outside than if one were inside and this occurs because the eye which stands outside in the air, its pupil contracts strongly and he who stands in a dark place, this pupil will make itself larger and with the smaller pupil the power diminishes and thus this power increases with the increase of its pupil and to the pupil of weak power every little obscurity appears dark to it and if it increases in power, ever great darkness will appear illumined to it.

7.2.v  Peashooter

    He mentions a fifth demonstration to confirm the link between pupil size and apparent size on L14r-13r (fig. 1050, 1497, 1502-1503):

To the extent that the light diminishes, to that extent does the pupil of the eye seen by this pupil increase.

Hence the eye which looks through a peashooter has a larger pupil than the other and it sees the object as larger and more clearly than does the other eye.

One makes a test of this by looking at a white line on a black background with two eyes of which one looks through the peashooter and the other through the luminous air.

    The test here described relates in turn to his subsequent experiments concerning the role of backgrounds in perception (see below p. ).

 

7.3  Theoretical demonstrations

    In addition to these five practical experiments he also pursues the connection between pupil size and apparent size in more theoretical terms as, for instance on D7r (1508) under the heading (fig. 1051):

(figure)

Figs. 1051-1052: Pupil studies on D7r and D4r.

How a larger pupil sees a larger object.

(To the extent that the pupil of the eye will be larger in shape, to this extent will the objects seen appear larger). This is proved because the pupil is entirely disposed with a same potential in seeing. Let us say that r is the pupil of the eye which receives the object g through a pyramid opposite and this pyramid measures the size in the section o on the little staff ab. Later go increases the pupil to the entire diameter mf. Now the object g will no longer make a pyramid but its species will come to this pupil by parallel lines and will be intersected by the same little staff ab and thus the image of the object g has grown in accordance with the growth of this pupil.

    On D4r (1508) he draws the pupil in relation to the cornea in the form of a cross-section (fig. 1052) accompanying which he offers a further theoretical demonstration:

If the cornea (luce) of the eye has its pupil which expands and contracts depending on the excess or lack of brightness which is placed in front of it, it is necessary that every other object...shows itself as greater or smaller to this pupil and let this be shown: let the cornea be hg and let its large pupil be am which sees the object qu on the convex side of the cornea at rq. Then let a be the diminished pupil and thus the object qu will be shown diminished on the convexity of the cornea in the space ps.

 

7.4  Madrid chapter

    In the Madrid Codex he develops his ideas on pupils in a series of paragraphs which amount to a chapter on the problem. This opens, on Mad II 25r, with a discussion of pupils of different shapes:

It does not injure the eye to have a pupil which is more squared or long than round, since each has the power to receive the species of objects positioned opposite. And /in order to see/ that it is true that such a form is not injurious, let an object be observed within the lids of the eyelids, practiclaly closed which will resist as it were the shape of the pupil in the above drawn shapes and does not vary in persepctive.

    A paragraph devoted to the case of cats follows:

The cat, in seeing and hearing has the first senses found among animals. And odour is practically the same as the aforementioned senses. And where it lacks visual power, it depends on hearing which always stands with /a/ ready ear, like a funnel, /prepared/ to receive the impressions of the vibrations made in the air, and sends them to the common sense along a broad way.

    He then turns to the human eye: "The eye of a man placed in the great light of the air or some other luminous body contracts the pupils and makes it of lesser power whence places of lesser light will appear tenebrous to it." On Mad II 25v he compared the amount of light seen by one and two eyes respectively (see below p. ), which leads to a comparison between small and large light sources:

A small and powerful light illumines a place in equal distance as much as a very large, weak one; the latter of which will be weaker than the former to the extent that the former is greater.

Hence the minimal light of the night, being in great quantity, will make itself equal to a small and little potent quantity of daylight.

(figure)

Figs. 1053-1055: Pupils by day and night on Mad. II 25v.

    No place in nocturnal times, is totally deprived of light, but it appears dark to diurnel animals.

    In the final paragraph he returns to the theme of changing pupil size: "Every pupil continually changes in diverse sizes, in diverse qualities of light or darkness, but above all the others, the owl makes the greatest change." In the right-hand margin he illustrates these changes in size of owls' pupils. In a first diagram he draws (fig. 1053) two tiny pupils marked b and c, connected with a large circle a which he describes in the caption: "a is the imprensiva in seeing luminous objects." Directly below he writes: "a is the imprensiva of the owl."

    This is followed by a second diagram (fig. 1054) in which the imprensiva a is dwarfed in comparison with the enormous size of the pupils in which are inscribed the words "nocturnal pupil." Finally, he makes a comparative diagram (fig. 1055) in which each of the pupils is drawn as three successively larger circles, marked a, b and c with the caption alongside: "a is the light of the sun; b is the daylight; c is the nocturnal light that the long-eared owl receives." Beneath this diagram is a further marginal note on human eyes: " Men overcome by excess light practically close the eyes, cutting off part of the pupil with the lids of the eyelids of the eyes, because by this means it is diminished as much as it can be." On Mad II 26r there are notes on painting. On 26v he returns to the connection between pupil size and light intensity, under the heading:

Of perspective.

The cornea (luce) of that eye which will have a greater pupil will see objects as larger. And this object will make itself larger to the extent that it is in a darker place and it will make itself smaller in places of greater light.

    He interjects a note why this is indirectly important for painting: "Even though this case is not to be enumerated among the precepts of painting, I nonetheless do not wish to exclude it because it is necessary for speculators." A general claim follows:

I therefore say that (every object of the eye is all in all and all in every part of the aforesaid pupil). When the aforesaid object is very luminous, the pupil, not being able to support it, makes itself so much smaller that the images of such a luminous object come to the pupil no less diminished in brightness than in size. Through which diminution the sense can support the brightness opposite it.

    By way of demonstration he cites his experiment of looking at a star through an aperture.

The example of that which has been said above is demonstrated and made manifest when one of the largest stars is seen through a small aperture made in a /piece of/ paper near the pupil of the eye, you will see such a star considerably diminished. And this occurs because all the pupil will not adopt itself in such vision but will adopt itself that much less than the whole to the extent that the star appears diminished, by that which it first appeared. And it is not because such an aperture intersects at the eye any part of the star seen, since, in addition to the quantity of the species seen, a great portion of the sky which surrounds it passes through this aperture.

    Immediately following he offers a second demonstration involving the candle experiment:

Again this can be demonstrated in another way with a second example, which helps to confirm the same conclusion, and this is that there is placed opposite the eye the light of a candle and behind this candlelight, or if you wish, at the boundaries beyond this, let the said star be seen. Now this star appears smaller to the extent that the pupil of the excess light opposite is diminished.

    At the bottom of Mad II 26v he outlines a third experiment:

Again if the eye on leaving a dark place suddenly encounters some brightness..., it will be seen at once that this brightness diminishes in light and size to the extent that the pupil makes itself smaller.

    On Mad II 27r, the folio opposite, he gives a more detailed account of his candle demonstration:

And if you wish to see a better and more palpable demonstration of what has been said place and raise the hand in front of the light of the candle opposite. And hold the eye firm on one of the larger stars and it will appear to you /that/ this star suddenly increases and suddenly diminishes. The increase occurs when you cover the light /of the candle/. The diminution occurs when the light is uncovered. And this occurs because, in covering the light, the pupil is enlarged and in uncovering this light, the pupil diminishes. And hence from what has been said, everything seen by this pupil diminishes its species together with the diminution of the aforesaid pupil. All the pupils of the eyes grow together with the brightness of the day and likewise they diminish as this brightness diminishes.

    He now returns to the case of pupils in nocturnal animals:

You see in nocturnal animals that they are endowed by Nature with a very large pupil which grows and diminishes in accordance with the brightness placed opposite. And not being able to diminish to such an extent by day that it is sufficient to support anything illuminated by the diurnal splendour, they are forced to live in dark places during this time. And at night their pupil multiplies to such a size that every great darkness appears to them to be a place that is strongly illumined.

    Some pupils of owls are, in turn, compared with those of men:

If one considers the size of the pupil of an owl at nighttime in proportion to the pupil of a man it will be found that this pupil of a long eared owl will be more than 40 times that of a man. And if beyond this there be considered the proportion of one and the other pupil, in comparison to their imprensivas, you will find that the imprensiva of man is more than 40 times that of the owl.

    In the margin he pursues this comparison between size of pupil and imprensiva:

The small imprensiva and the large pupil render the same objects 4 times larger than to double the imprensiva and a pupil half as large.

Among equal imprensivas and pupils, equal objects render themselves equal to these. Unequal imprensivas in equal pupils, render equal objects strongly unequal.

    Beneath this he draws a rough sketch of a small pupil and large imprensiva (fig. 1056) and with this his excursus on pupils ends.

 

7.5  Comparative Studies of Pupils in Man and Animals

    The comparisons between pupils in owls and men in the Madrid passages just cited reflect a theme that fascinates Leonardo. Perhaps the earliest extant note on the problem is on H86/38/r (1494):

All things seen appear larger at midnight than at midday and larger in the morning than at midday.

This happens because the pupil of the eye is considerably smaller at midday than at any other time.

To the extent that the eye or pupil of the long eared owl has a greater proportion than the animal of man, to this extent does it see more light by night than does a man. Whence at midday it does not see a thing if it does not diminish its pupil and similarly it sees things larger at night than by day.

    On CA262rd (1506-1508), on a folio where he also discusses camera abscuras (see above p. ), he begins with variations in the human pupil:

If the...darkness of the night is 100 degrees of darkness than in the evening and the eye of a man doubles /the size/ of its pupil, this darkness diminishes by half to this eye because, having doubled half of its visual power, there now remain for it 50 degrees of obscurity of darkness.

    This he compares with the case of an owl:

figure)

Figs. 1056-1061: Pupils of different shapes and sizes. Fig. 1056, Mad II 27r; fig. 1057, Mad II 25r; figs. 1058-1059, CA262rd; fig. 1060, BM64v; fig. 1061, G44v.

And if the eye of a long-eared owl increases its pupil one hundredfold in the aforesaid darkness, the visual power increases one hundredfold, which are 100 degrees of visual power /which have been/ gained and because equal things do not exceed one another, the bird sees a hundredfold more in darkness with its pupil, than by day with its pupil diminished by 99/100.

    An objection is now raised and dismissed:

And if you said that such animals do not see light by day and therefore remain closed, it is replied that the bird only closes it by day in order to liberate itself from the concourse of the birds which, in a great multitude always surround it with great noise, and often they would be dead if they did not hide in the grottoes and caverns of the high rocks.

    In the right-hand margin he draws both a small pupil of a man and the potentially large pupil of an owl (fig. 1059) which he identifies and beneath which he adds a caption:

The pupil c is its size during the daytime, that is, in the greatest brightness of the day.

Ac is how it grows in the greatest darkness of the night and thus it goes increasing /or decreasing/ to a greater or lesser quantity depending on the greater or lesser obscurity of the light.

    In the second portion of the text on CA262rd he considers the pupils of the leonine species and problems of pupils of different shapes:

Among nocturnal animals only the leonine species increases and decreases its pupil, varying in shape, such that when it is in its ultimate diminution it is of a long shape; when it is midway, it is of an oval shape and when it is at its ultimate size, it is of a circular shape.

(figure)

Figs. 1062-1063: Inversion in a slit-like pupil on CA262rd.

    In the margin he draws a slit pupil in the shape of a thin rectangle (fig. 1058). In the main text he then considers the consequences of such a pupil for the visual process:

It is to be doubted whether, when this pupil is of a long shape, whether round or spherical things appear long or round.

It is proved that as many are the distances from the spherical object, so many are the varieties in which the shape of this spherical object transforms itself to the eye.

    To illustrate this he draws a small marginal diagram (fig. 1062) followed by a larger one which intrudes on the text space (fig. 1063). Around this he explains:

It is true that, after the concourse of the pyramidal rays joining ar at o, ... they pass to nm and switch the sides of the shadow of this spherical body because t, the lower part of this body becomes /the/ upper and s the upper part of this body becomes the lower at n.

    In this context the reason for his studies with slit-shaped camera obscuras becomes clear (see above p. ). Despite all these studies he remains unsatisfied. On CA360RC (1508-1510), for instance, he asks anew: "Why the pupil becomes smaller the more light it has in front of it and similarly, in the opposite /situation/, expands in the dark?". On W19042r (K/P 42r , 1489-1510), he offers an answer, beginning with two claims about nocturnal animals:

The pupil of nocturnal animals goes varying from a large to a larger quantity depending on the great or greater darkness of the night.

The pupil of these nocturnal animals again varies from smaller to smaller depending on the great or greater brightness of the day.

    This leads to comments concerning images being "all in all the eye."

From that which has been said it is concluded that these nocturnal animals are always with an equal potential of visual power in all the varieties of brightness or darkness which can happen in times of day or night.

The visual power is all in all the pupil and all in every part.

It follows that half of the pupil sees the object integrally as if it were entire.

    He now returns to his connection between pupil size and the apparent size of objects:

To the extent that the pupil is of greater quantity to that extent will it see its object of greater size and clarity and likewise, conversely: to the extent that it will be less, to this extent will it see the object as smaller and more obscure.

It follows that, closing one eye, the visual power is diminished by half and this test is made with luminous bodies such as the sun, moon and stars and also a light or fire.

    In his final example on this folio he considers an experiment comparing effects of monocular and binocular vision (see below p. ). He pursues his comparative studies of senses in man and animals on W19030v (K/P 72v, 1489-1510):

I have found in the composition of the human body that, as in all compositions of animals, it is of blunter and grosser sentiments. Hence it is composed of instruments which are less ingenious and of places less capable of receiving the power of the senses. I have seen in the leonine species /how/ the sense of smell has part of the substance of the brains and descends to the nostrils, capable receptacle/s/ for the sense of smell which enters through a great number of cartiligenous pores with enough ways to reach the aforementioned brain.

    A comparison of eyes in lions and men follows:

The eyes of the leonine species have a large part of their head as their receptacle and the optical nerves are joined directly with the brain; the contrary of which is seen in men, because the receptacles of the eyes are a small part of the head and the optic nerves are thin and long and weak and by means of a weak operation one sees day with them and night worse. And the above mentioned animals see better by night than by day and the sign is seen becasue they prey by night and sleep by day as the nocturnal animals do also.

    This leads to a comparison of their pupils:

The luce or pupil of the homan eye, in its expansion and contraction, increases and decreases by half its size. And in the nocturnal animals it dminishes and increases it by more than a hundred times and this is seen in the eye of the long-eared owl, a nocturnal bird, when one brings a lighted torch near to its eye and more, if you have it look at the sun. Then you will see the pupil, which at first occupied the entire eye, dminish to the size of a grain of millet and in this diminution it bears comparison with the pupil of a man and things clear and lustrous appear to it /to be/ of the same colour, as they appear at that time to a man and the more so, the more the brain of this animal is less than the brain of a man. Whence it happens that, incresaing this pupil a hundred times more than that of a man in nighttime, it sees a hundred times more light than man, in such a way that the visual power is not then overcome by the nocturnal darkness and the pupil of man, which only doubles its quantity, sees little light, is like the bat, which does not fly in times of too much darkness.

    On D5v he continues this discussion, beginning with two chapter headings in the margin: "Why nocturnal animals see more by night than by day? On the eye of man in comparison with his brain." Opposite this is an introductory paragraph:

There occurs the discourse of the eyes of nocturnal animals, which see better by night than by day. And this occurs because the size of their eyes is larger than the whole of their brain and /this occurs/ maximally in long-eared owls, tawny owls, barn owls, little owls, common owls and the like which does not happen in man who has a larger brain than any other terrestial animal incomparison to his eyes and he sees little light after day/time/.

    The folio ends with the instruction "turn the page" to 5r. Here the comparison between man and nocturnal animals is reformulated:

There follows on the eye of nocturnal animals which see more by night than by day and this in large part occurs as was said above. Because there is a much greater difference in the increase and decrease of their pupils than in diurnal animals. For if the pupil of a man doubles the size of his pupil at night, that is to say, /it is/ four times that /which it is/ by day, the diameter of the pupil of the horned owl or long-eared owl increases 10 times /over/ that by day, which is to say, a total of 100 times the pupil of the daytime.

    A comparison of imprensivas follows:

Moreover, the ventricle placed in the brain of man, called the imprensiva...is more than ten times the size of the entire eye of man, of which the pupil where vision is caused is less than a thousandth part of this eye. And in the long-eared owl the nocturnal pupil is considerably larger than the ventricle of the imprensiva positioned in its brain. Whence man has a greater proportion of imprensiva relative to his pupil (luce) - the imprensiva being ten thousand times more...than the pupil - than the horned owl in which /the imprensiva/ is practically equal /to the pupil/. And this imprensiva of man, in comparison tot hat of the long-eared owl is like a large room which has light through a little aperture in comparison with a little room completely open, such that in the large room night comes at noon and in the little, open one, day comes at midnight, the weather not being cloudy and with this one will show more powerful causes through the anatomy of the eyes and impressive of the two animals, that is, of man and the horned-owl.

    This discussion is again summarized by two marginal notes:

On the great variety that nocturnal animals make from their largest pupil of the eye at night to the smallest pupil by day.

Proportion of the ventricle of the imprensiva, positioned int he brain of animals, with their pupil.

    On BM Arundel 64v (1509) he explores how a bird's eye and pupil opens and closes (fig. 1060):

Abn is the lower lid which clsoes the eye from below upwards with an opaque lid; cnd closes the eye inside from behind a transparent lid.

    It closes from below because it descends from above.

When the eye of birds closes itself with its two lids it first closes the secundina which closes from the tear duct to the rear of the eye and the first closes itself from below above and these two intersecting motions first occupy the tear duct, because as we have already seen, they are secured in front and below and the part above only serves for the dangers of predatory birds which descend from above below. And first they cover the tunic near the tail end, for if the enemy comes /from/ behind, he has the opportunity of fleeing in front and again he holds the tunic called secundina which is transparent, for if he did not have this shield,...he could not hold his eyes open against the wind which percusses his eye in the fury of his swift flying. And his pupil grows and diminishes in seeing a lesser or greater light, that is, brightness.

    He takes up the theme of comparative pupil sizes anew on G44r (c. 1510-1515) in a passage headed:

(figure)

Figs. 1064-1067: Inversion of the pupil on CA190vb.

On the eyes of animals.

The eyes of all animals have their pupils which expand and contract of themselves depending on...the greater or lesser light of the sun or other bright body. But in birds this makes a greater distance and maximally in the nocturnal ones such as long-eared owls, barn owls and tawny owls which are a type of small owl. In these the pupil grows in such a way that it practically occupies all of the eye and diminishes to the size of a grain of millet and always maintains a circular shape. But the leonine species such as panthers, leopards, lions, wolves, lynxs and spanish cats and other similar /animals/ diminish their pupil from a perfect circle to a disangular figure, that is this. And his is shown in the margin.

    In the margin he draws (fig. 1061) two sets of three pupils marked omn and caa respectivally, the first set representing the pupils of owls, the latter, pupils in the leonine species. Above these he writes a marginal note:

Make an anatomy of various eyes and look at which are the muscles that open and close the aforementioned pupils of the eye of animals.

    In the main text he compares these with human pupils:

But man, having weaker sight than any other animal is less offended by excessive light and expands less in dark places. But among the eyes of the above mentioned nocturnal animals, the long-eared owl, a horned bird, which, in the species of nocturnal birds, augments its visual power so much that in the minimal nocturnal light (which we would call darkness), it sees well enough with more vigour than we in the splendour of midday, in which such birds are hidden in dark places and if perchance

    Having reached the end of the folio he continues in the lower half of the right-hand margin: "they are constrained to go out into the illuminated air of the sun and they diminish the pupil by so much that the visual power diminishes together with the quantity of such light." A late diagram on CA243va (c. 1513) which, as Pedretti has s hown, is connected with W12443r (figs. 1068-1069) further illustrates connections between the pupil and camera oscura (cf. figs. 1064-1067).

 

7.6  Towards Quantification

    Throughout the above mentioned notes Leonardo is tending towards a quantitative approach to the problem. Hence on Mad II 25 he alludes to how a man's pupil expands twofold at night, whereas, in a long-eared owl, the pupil expands one hundredfold. On CA262rd he also uses these ratios, once more on W19030v (K/P 72v, 1489-1510) and again, in modified form, on D5r (1508) where he claims that a man's pupil expands twofold but its power fourfold, whereas the pupil of a long-eared owl expands tenfold and its power hundredfold. On D5r his love of successive ratios leads him astray. He claims, for instance, that the imprensiva is 10 times the size of the eye and the eye, in turn 100 times the size of the pupil, which would mean that the imprensiva is 10,000 times larger than the pupil: clearly an exaggeration.

    Leonardo's problem is that although his thoughts are coherent, he is disorganized in presenting them. This weakness prevents him from retrieving efficiently what he has already done and building on his earlier efforts. As a result the quantitative urge comes and goes without resulting in ever more accurate observations and clearly organized tables.

(figure)

Figs. 1068-1069: Inversion int he eye on CA243va and W12443r.

 

7.7  Rules

    In the end he contents himself with a series of general rules concerning the relations of pupil size, apparent size and apaprent brightness. The earliest hint of such a rule can be traced back to Forst III 36r (1490-1493) under the heading:

What thing is better seen.

Among walls of equal size and quality which are seen beyond the extremities of an opaque object placed in front of it, that part of this wall will appear more illumined which is seen by a greater amount of pupil.

    This rule concerning size he expresses more clearly on Mad II 127v (1503-1505):

On painting, that is, on the eye.

The sizes of things seen appear as many as are the sizes of the pupils to which these things are represented.

    At this point he is still apologetic concerning its relevance for painting and adds (see above p. ):

Even if these speculations be superfluous for practitioners, it did not appear to me that they were to be excluded because they often give admiration to ingenious speculators.

    By 1508, on F37r, he carefully numbers his rules:

First: that pupil which will be less in a same quantity of eye will see the object smaller and darker.

Second: among objects of equal distance, the smaller sends a smaller angle to the eye and the larger a larger.

    By 1513-1514, on E17v, these ideas emerge in a series of six propositions under the heading:

Painting.

First: The pupil of the eye diminishes its quantity by the extent to which the luminous body increases which impresses itself in it.

Second: The pupil of the eye increases to the extent that the brightness of the day - or other light which impresses itself in it diminishes.

Third: The eye sees and understands the objects which stand as its objects /of sight/ the more intensively, to the extent that the pupil dilates itself more and this we prove through nocturnal animals such as cats and other flying creatures such as the long-eared bat and the like, the pupils of which undergo a very great variation from large to small in the darkness or light.

Fourth: The eye placed in the illuminated air sees darkness inside the windows of illuminated houses.

Fifth: All colours positioned in dark places appear to be of equal darkness among one another.

Sixth: But all colours positioned in luminous places will never vary from their essence.

(figure)

Figs. 1070-1072: Eye as a concave mirror. Figs. 1070-1071, Forst. III 24r; fig. 1072, Forst. III 56r.

    His pupil studies had begun as a strictly optical problem. In the late period they have become integrated within his concept of painting.

 

8. Uvea

    In terms of modern anatomy the uvea or grape-like tunic is the pars iridics retinea directly behind the iris. Leonardo's conception of the uvea is different, namely, as a reflecting sphere surrounding the vitreous body - which he calls the albugineous humour - and concentric with the crystalline sphere, (D7v, 1508). He mentions the term uvea at least 16 times and illustrates it no less than seven times (figs. 1072-1076, Chart 24). From these diagrams it is clear that the position of the uvea in his interpretation corresponds roughly to the actual site of the retina.

 

8.1  Function of the Uvea

    In various diagrams he depicts the uvea as if it were a mirror which serves to reflect rays either towards the crystalline sphere, as on Forst III 24r (figs. 1070-1071, c. 1490-1493), Forst III 56r (fig. 1072, 1490-1493) and K119/39/ (fig. 1079, 1504-1509) or directly towards the optic nerves, as on D10r (fig. 1076, 1508). He is interested in the possibility that the uvea may be more than merely a mirror. On DA190vb (1505-1508), for instance, he asks, "whether the image (eidola) is in the concavity of the uvea or truly in the crystalline sphere and not in the uvea." On this same folio he records his intention to "make such an eye and of glass as a natural one" (fig. 1074) and makes another drawing (fig. 1075) in which he notes that "a sees the surface of its sphere nSt tinged by the darkness of the uvea."

(figure)

Figs. 1073-1076: Reflection from the uvea. Fig. 1073, CA210va; figs. 1074-1075, CA190vb; fig. 1076, D10r.

Chart 24: List of Leonardo's uses of the terms uvea, spera (omore) cristallina, vitrea, albuginea, orbit, optic foramen and optic chiasma.

(figure)

Figs. 1077-1081: Eye as a concave mirror. Figs. 1077-1078, CA237ra; fig. 1079, K119/39/v; figs. 1080-1081, D7v.

    On D7v (figs. 1080-1081) he explores further the role played by the uvea while discussing the possibility that the visual power is situated in the crystalline humour:

And if such a power...is in the centre of the crystalline humour it takes the species with their surface and they are referred from the surface of the cornea (luce) where the objects are mirrored...or they are reflected from the surface of the uvea which is boundary and container of the albugineous humour /i.e. the vitreous body/, which has opacity behind the...transparency of the albugineous humour, as when the capacity of lead is placed behind the transparency of glass in order that things can be better mirrored at the surface of such glass. But if...the visual power is at the centre of the crystalline then all the things which are given to it fromt he surface of the cornea (luce) of the eye will appear to it in the true site where they are and they will not switch sides from right to left and they appear larger as is proved in perspective. And if such a crystalline sphere takes those species reflected from the concavity of the uvea, this iwll take them right side up...even though the uvea is a concave mirror and it will take them right side up because the centre of the crystalline sphere is concentric with the centre of the sphere of the uvea.... And it is true that the species passing to this uvea, which are outside the eye pass to this uvea through the centre of the crystalline sphere and, joined to the uvea, they are reversed and those which pass to this uvea without passing through such a /crystalline/ humour.

    On D10r (1508) he explains why he rejected the possibility that the uvea might be the seat of the visual power, under the heading:

Doubt concerning the impression of the images (eidola) in the eye.

There was a doubt concerning the situation of the image (eidolum) in the eye, that is, if it appears in the concavity of the uvea p or in the convexity of the crystalline sphere n. But soon I confirmed that if it were impressed in the concavity of the uvea that such an image (eidolum) whould not be reflected to the power since its angle of incidence would not be equal to the angle of reflection.

    This leads to his own theory concerning what actually happens in the eye:

And therefore it can be judged that such an image (idolum) from c coming to the pupil through the line cx and entering the pupil through the line xm, percusses the crystalline sphere and can rebound to p /in the/ concavity of the uvea and can also pass to the crystalline sphere through the line nrt and this t is to be understood as the front of the optic nerve st which penetrates somewhat into the crystalline sphere and thus c sends its image to t which it could not do if it impressed itself in the concavity of the uvea at the site p.

    Ultimately the uvea may reflect images but that is all.

 

9. Crystalline Humour

    He refers to the crystalline humour at least 6 times and to the crystalline sphere no less than 16 times. In his early notes he tends to equate the crystalline humour with the aqueous humour. This he suggests on CA85va (1503-1504) and illustrates on CA204rb (1490-1492) where he points out that the crystalline humour occupies the "quarter bef" (fig. ). Similarly on A78 (1492) he refers to the "subtle humour called crystalline that stands in the cornea (luce). Later he conceives of the crystalline lens as a sphere at the centre of both the vitreous body and the eye. From Galen11 through to Pecham,12 various authors (cf. figs. 957-962) had situated the crystalline lens at the centre of the eye. Leonardo clearly intended to study the rpecise position of the crystalline more carefully. On CA345vb (c. 1508), for instance, he notes:

Write in your anatomy what proportions the diameters of all the spheres of the eye have and what distance the crystalline lens has from them.

    In the extant notes there is no record of his having carried out this plan. He does, however, provide a series of illustrations showing the crystalline sphere in the centre of the eye on K/P 118v (W19150v, fig. , 1508-1510); Manuscript D2v, 3v, 7v, 8r and 10r (figs. , 1508). On D8r he begins writing "crystalline," crosses this out and replaces it with "vitreous." On both D8r and 3v crystalline and vitreous are synonymous.

 

9.1  Function of the Crystalline Humour

    He assumes that the crystalline lens is like a sphere of water which refracts images at its surface and then inverts them. He describes the general properties of such spheres of water and gives instructions concerning their construction. There is no record of his making quantitative records of the refractive properties of such spheres of water (see below pp. ). In a majority of cases (figs. ) he assumes that an inversion of images occurs at the centre of the crystalline sphere. In Manuscript D he explores alternatives. On D3r, for instance, he draws (fig. ) two rays being refracted at the front of the crystalline sphere, passing through it along parallel lines and being refracted inwards on re-entering the vitreous humour. On D3r, he also considers the possibility that images could pass through the crystalline without any refraction. On four other occasions, D3v, 8r, 8v and 10v (figs. ) he considers an alternative that the crystalline sphere might refract images at both its front and back surfaces without actually inverting them. On each occasion he represents this refraction in slightly different terms. On D5r he also explains why he believes that the crystalline lens is capable of varying its density:

the crystalline humour...which is positioned inside the pupil condenses itself in the face of...lucid things and rarifies itself in facing dark things and it is shown that this is true by closing an eye, because the species of things which remain /as after images/ are seen as dark and the dark objects show themselves as bright and this happens more in weak eyes than in strong ones and of this I shall speak more fully...in its /proper/ place.

 

10. Vitreous Humour or Body

    In the early extant notes he has no term for the vitreous humour. In the Manuscript D (1508) he refers at least three times to an albugineous sphere and no less than 8 times to an albugineous humour. In most cases (figs. ) this albugineous humour is synonymous with what would today be termed the vitreous humour or vitreous body. In the Manuscript D he also refers at least once to an omore vitrea and no less than 15 times to a spera vitrea. On D8r, he begins by writing "crystalline," crosses this out and writes "vitrea." Diagrams on D8r, 3r, and 3v (figs. ) confirm that, in his mind, spera vitrea, is synonymous with crystalline sphere and not the vitreous humour in the modern sense.

 

10.1  Function

    In the early notes the role played by the vitreous humour in the visual process is neither discussed nor illustrated. In the Manuscript D he shows (figs. ) rays passing directly from the aqueous humour in the cornea, through the pupil and into the vitreous humour without any refraction. On D3v, 8r, 8v and 10v (figs. ) he draws the rays as being refracted in passing from the vitreous to the crystalline, then refracted anew in passing from the crystalline back into the vitreous humour and intersecting a second time in the vitreous humour before entering the optic nerve. Hence the vitreous humour becomes the place where images are re-inverted in order to reach the brain right side up.

 

11. Retina

    In Leonardo's models of the eye the uvea takes the place of the retina. But its function remains very different. The uvea as he conceives it merely reflects images like a mirror: it does not record images in the way the retina is now known to do.

(figure)

Figs. 1082-1084: Orbit and optic foramen on K/P 32v, 42v, 71v.

 

12. Orbit

    He refers to the orbit or eye-socket as the case of the eye (cassa dell'occhio) on at least three occasions. In addition he draws it both frontally and from the side a number of times (figs. 1082-1091, Chart 24). On W19058v (K/P 42v, 1489-1510) he includes both the superior and inferior orbital fissures and indicates the superorbital and infraorbital foramina (fig. 1083). He does not discuss the orbit's function.

 

13. Optic Foramen

    On W19059v (K/P 40r, 1489-1510) he refers to the optic foramen as the "aperture of the case of the eye" (buso della chassa dell'ochio). Although he has no technical term for the foramen, he shows it clearly in a number of his anatomical drawings (figs. 1092, 1093, Chart 24).

 

14. Second or Optic Nerve

    In his extant notes he refers to optic nerves at least 21 times (Chart 24). A majority of these obviously refer to the second nerve. In his drawings he indicates the path of this second or optic nerve at least 11 times (e.g. figs. 1113-1119). On W19057r (IK/P 43r, 1489-1510), he shows the optic nerves (fig. 1092) protruding from the optic foramina. The precise origin of the optic nerve remains a problem for him. In his early drawings on W12627r, 12626r (K/P 4r, 6r, figs. 1100, 1101, 1485-1487), and BM711v (fig. , 1492) he represents this nerve as originating directly behind the pupil. Later, probably as a result of having studied Pecham13 (fig. ), he shows it as beginning behind the crystalline sphere (figs. 1104-1105). By 1508 he tends to show the optic nerve as originating directly what we would term the retina (figs. 1117-1119).

(figure)

Figs. 1085-1091: Lateral views of the orbit foramen. Fig. 1085, K/P 2r; ;figs. 1086-1087, K/P 3r; fig. 1088, K/P 4r; fig. 1089, K/P 6r; figs. 1090-1091, K/P 40r.

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Figs. 1092-1094: Lateral views of the orbit and optic foramen, with optic nerves crossing at optic chiasma. Fig. 1092, K/P 42r; figs. 1093-1094, K/P 43r.

 

14.2  Function

    He makes some comparative studies of optic nerves. On W19030v (K/P 72v, 1489-1510), for instance, he notes that in the leonine species "the optic nerves are immediately joined to the brain" and he contrasts these with man whose:

optic nerves are thin, long and weak. As a result one observes that they work weakly by day and worse by night and the aforesaid animals see better by night than by day. And a sign of this is that they hunt their prey at night and sleep in the day as do nocturnal birds also.

    On W19052r (K/P 55r, 1489-1510) he notes that the function of the optic nerves is to serve the visual power. On D3v, 7v and 8r (1508) he locates the visual power at the entrance of the optic nerves. Precisely how images are conveyed through the optic nerves to the senso commune and the imprensiva he does not explain.

 

15. Optic Chiasma

    He does not have a specific term to describe the optic chiasma. Four early drawings (figs. 1082, 1100-1102) confirm that he was initially unaware of its existence. Following his anatomical studies in the period 1506-1508, he indicates the position of the optic chiasma clearlty (figs. 1104-1105, 1113-1119). In the extant notes he makes no conjectures concerning its function.

(figure)

Figs. 1095-1096: Lateral views of the orbit and optic foramen on K/P 43.

 

16. Optic Tract

    He also has no term for the optic tract, but in the period after 1505 he draws it on at least nine occasions (figs. 1104-1105, 1113-1119).

 

17. Third or Motor Oculi Nerve

    His interest in the third or motor oculi nerve is first recorded in a note on W19059v (K/P 40v, 1489-1510):

What nerve is the cause of movement of the eye and makes the movement of one eye draw the other?

Of closing the eyelids
Of raising the eyelids
Of lowering the eyelids
Of shutting the eyes
Of opening the eyes.

    On W19052r (K/P 55r, 1489-1510) he draws this nerve, (also called the oculomotor nerve), clearly (figs. 1104-1105). On W19116-7r (K/P 115r, 1508-1510) he makes a further note:

Search for the motor nerves of the eyes from all aspects and consider if the principal ones are 4, or more or less, because in all the infinite motions 4 nerves do all, because, as soon as you leave the jurisdiction of one of these 4 nerves, you acquire favour and aid from a second nerve and thus it continues.

 

18. Ophthalmic Nerve or First Division of the Fifth or Trifacial Nerve (n. trigeminus)

    He has no specific term for this nerve, also known today as the ophthalmic division of the trigeminal nerve, but, nonetheless, draws it on both the Weimar sheet (fig. 1117) and W19052r (K/P 55r, figs. 1104-1105, 1489-1510). In the extant notes he does not discuss the function of this nerve.

(figure)

Figs. 1097-1099: Traditional versions of the three ventricles. Fig. 1097, Albertus Magnus, Philosophiae pauperra, 1493, fol. C4v; fig. 1098, Gregor Reisch, Margarita philosophica fig. 1099, Leonardo, W12603r.

Chart 25: List of Leonardo's uses of the terms ventricolo, imprensiva, senso comune, memoria, giudizio and virtu visiva.

(figure)

Figs. 1100-1103: Early drawings of eyes, nerves and ventricles on K/P 4r, 6r, 32r and Forst. III 28r.

 

19. Ventricles

    Mediaeval authors such as Albertus Magnus assumed that the ventricles were circular cavities14 (fig. 1097), Gregor Reisch also assumed this in his Margarita philosophica15 (fig. 1098). Leonardo's early drawings (figs. 1099-1102) stand clearly within this tradition. Sometime between 1506 and 1508, however, he injects wax into the ventricles and thus arrives at a much more accurate impression of their shape (figs. 1106-1110). He only rarely uses the general term ventricle (e.g. D5r, 1508), but has his own terms for the lateral, third and fourth ventricles respectively.

 

19.1  Lateral Ventricle

    In an early drawing on W12626r (K/P 6r, fig. 1101, 1485-1487) he indicates the lateral ventricle as seat of both the intellect and the imprensiva. For him the imprensiva is where the images are impressed. He uses the term imprensiva at least 43 times and illustrates it 9 times (e.g. figs. 1109-1112, Chart 25). He does not discuss the function of the imprensiva in detail. Nonetheless, on Mad II 24r and 25v, he notes that two eyes affect an imprensiva twice as much as does one eye, and one Mad II 27r he considers the effects of relative sizes of imprensiva and pupil, claiming that the imprensiva in man is 40 times the size of an owl's imprensiva, (see above p. ). These comparisons he pursues on D5r (1508) where he claims that the imprensiva in man "is more than ten times the size of the entire eye of man and the pupil in which sight has its origin is less than a thousandth part of the eye, whereas the pupil of the long-eared owl, at night, is considerably larger than the ventricle of the imprensiva situated in its brain."

(figure)

Figs. 1104-1105: Ocular orbits, nerves and chiasma on K/P 55r.

 

19.2  Third Ventricle

    On W12626r (K/P 6r, 1485-1487) he shows the third ventricle as seat of both the will (volunta') and the senso comune. He uses the term senso comune at least 24 times (Chart 25). In his anatomical studies he sets out to define precisely where the senso comune is situated. On W19058r (K/P 42r, fig. 1093, 1489-1510), for instance, he notes:

The confluence of all the senses has below it in a perpendicular line the uvula where one tastes food at a distance of two fingers and it is directly above the wind pipe of the lung and above the orifice of the heart by the space of one foot. And it has the junction of the bones of the head /bregma/ half a head above it; and in front of it on a horizontal line is the lacrimator of the eye /nasolacrimal duct/ at one-third of a head. And being it is the nape of the nect at two-thirds of a head. And at the sides the two temporal pulses at equal distance and height.

    On W19057r (K/P 43r, fig. 1094, 1489-1510), he locates the senso comune clearly with a drawing and the caption: "where the line am is intersected by the line cb there the meeting of all the senses is made."

19.2.i.  Function

    On CA90rb (c. 1490) he discusses the function of the senso comune and its relation to both the imprensiva and the memory:

The senso comune is that which judges the things given to it by the other senses. The ancient speculators concluded that that part of the judgment which is given to man, is caused by an instrument, to which the other 5 refer via the imprensiva and to this instrument they have given the name senso comune and they say that this sense is situated in the middle of the head between the imprensiva and the memory. And they use this name senso comune only because it is the common judge of the other 5 senses, that is, sight, hearing, touch, taste and smell, The common sense moves via the imprensiva which moves through the similitudes of things given to it by the superficial instruments, that is, the senses which are positioned in the middle between the exterior objects and the imprensiva and similarly the senses are moved through objects. Surrounding objects send their similitudes to the senses and the senses transfer them to the imprensiva. The imprensiva sends them to the senso comune and from this they are established in the memory and are retained more or less in accordance with the importance and power of the thing given. That sense is more speedy in its function which is closer to the imprensiva and the eye /which is/ superior to and leader of the others is the only one of which we shall treat....

(figure)

Figs. 1106-1108: Ventricles in ground plan on K/P 104r.

    He pursues this discussion on W19019r (K/P 39r, 1489-1510) under the heading:

How the 5 senses are functions of the soul.

The soul appears to reside in the judicial part and the judicial part appears to shere all the senses come together, which is called senso comune and it is not all in all the body as many believed, but all in this part. For if it were all in the whole and all in each part it would not have been necessary to make the instruments of the senses converge to one and the same concourse in one place only. On the contrary it would have sufficed for the eye to perform its sensory function on its surface and not transmit the similtudes of things seen by way of the optic nerves to the senso comune, because the soul, for the aforesaid reason, would be unable to comprehend them on the surface of the eye.

(figure)

Figs. 1109-1112: Ventricles of the brain based on wax injection experiments. Figs. 1109-1110, K/P 104r; fig. 1111, K/P 127r; fig. 1112, CA212vb.

    From these passages it is clear that the third ventricle, which Leonardo terms the senso comune is also the seat of the judgment. At an earlier date he had been non-committal concerning the precise location of the judgment. On BM220v (1500-1505), for instance, he had noted:

If the judgment of the eye is inside it, the straight lines of the species are bent on its surface because they go from rare to dense.

    Among Mediaeval writers such as Nemesius and Macrobius there had developed a view that the senses are reliable,16 and that only the judgment was deceptive. This attitude also emerges in Leonardo's later notes. On TPL65a (1505-1510), for example, he points out that: "There is nothing which deceives us more than our judgment either in giving a bad opinion of our works or in judging as good the things of our enemies or our friends." On CA154rb (1508-1510, cf. 154rc) he openly contrasts the reliability of of experience, i.e. the senses, with the deceptiveness of judgment:

Experience is never deceived, but only your judgments are deceived, promising from such an effect that which is not caused in our experiments.

    On CA29va (1509-1510) he goes on to compare the deceptions of judgment with deceptions of vision:

(figure)

Figs. 1113-1118: Eyes, optic nerves, chiasma and three ventricles in context. Fig. 1113, K/P 113r; figs. 1114-1115, K/P 103r; fig. 1116, K/P 113r; fig. 1117, K/P 54-55 (Weimar); fig. 1118, K/P 103r.

(figure)

Fig. 1119: Eyes and brain on K/P 54-55 (Weimar).

Our judgment does not judge things made at various distances of time in their usual and proper distances because many things which happened many years ago appear near and close to the present and many things close (to the present) appear old, together with the age of our (summer) youth. And so too does the eye with distant things which, being illuminated by the sun appear close to the eye and many nearby things appear distant.

 

19.3  Fourth Ventricle

    On at least 6 occasions he designates the fourth ventricle as the seat of memory (Chart 25, e.g. figs. 1110, 1117).

 

20. Visual Power

    Leonardo mentions the term visual power (virtu visiva) at least 66 times and an alternate form, (potentia visiva) no less than four times. Its precise nature at first remains ambiguous: is it active int he manner of the ancient theory17 which held something active enamates from the eye or is it passive like a screen or film which records images? At the outset in 1492 Leonardo assumes that the visual power is situated in a point on or within the pupil. Various experiments (see above ) persuade him that this power is not only in one point but "all in all and all in every part" of the pupil. At the same time, his general conception of physics leads him, on D1r, to argue:

Why Nature did not make the visual power equal in power in all its parts.

Nature did not distribute power equally in the visual power, but gave this power increasingly greater power towards its centre and this was done in order not to break the law given to all other powers in which strength progressively increases towards their centres. And this is seen in the percussion of any body, in the suspension of the arm of balances where the poise diminishes in gravity as it approaches its fulchrum, it is seen in columns, walls and pilasters; it is seen in heat and in all the other natural powers.

    Meanwhile, in the period 1505-1508 he explores further alternatives: that the visual power might be situated in the crystalline sphere, in the uvea or at the beginning of the second or optic nerve (Chart 25). He decides finally that it must be situated at the beginning of the optic nerve, and that the visual power is not something which emanates from the eye, but rather something which passively waits for images to come to it. Precisely how it conveys the information of those images to the brain, he does not explain.

 

21. Conclusions

    With respect to the eye Leonardo wishes to reject the authority of previous authors and base his claims strictly on experience (CA119va). This is not to say, however, that he ignores earlier sources entirely. We know that he studied Pecham's Optics directly (see above p. ) and hence it can hardly be a coincidence that there are very close parallels between Pecham's notions that the optic nerve protrudes into the crystalline lens and Leonardo's opinions. A detailed analysis of each part of the visual process discussed or illustrated by Leonardo, reveals how his attention paid to different parts varied enormously (see Chart 20). In rare cases such as the "orbit" or "optic chiasma" he has no term for a part although he illustrates them beautifully. In most cases he mentions a term less than 25 times. He uses the term senso comune 25 times, imprensiva, 43 times; and both virtu visiva and luce 70 times. By far, his most frequently used term is popilla (253 times).

    It was noted that the meaning of both luce and popilla remain ambiguous. Both terms embrace a series of connotations which range from pupil, through cornea to the eye in general. The reason for their surprising importance in the notebooks is because Leonardo believes that variations in pupil size play a key role in all estimates of apparent size.Although Leonardo pleas for an experimental approach to vision, it is important to note that he is only able to carry this out in stages. By 1490 he has analysed the orbit and optic foramen. (This provided no difficulty because skulls were relatively easy to come by.) In the period 1506-1508 he makes his experimental demonstrations concerning the optic chiasma and optic nerves, as well as the ventricles.

    By 1504-1509, he also interested in dissecting the interior of the eyeball itself. But this he appears never to have accomplished. Was it from lack of time? Or was he not allowed? We know that he had trouble with permission to do anatomy in the late period (CA182v). One thing is fairly certain. In the early period, when there may have been more opportunity for anatomical study, Leonardo had little interest in the structure of the inner eye. Only gradually did he recognize that the nature of the visual process behind the pupil was a problem. And it may well be that by the time he saw the problem fully, the opportunities for studying it were no longer fully there. How he came to see that the visual process was a problem is the subject of the next chapter.


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Last Update: July 2, 1999