Part Three, Chapter 4: Optimal and Minimal Conditions of Vision

1. Introduction 2. Central Ray 3. Visual Field 4. Occlusions 5. Objects too near

6. Objects too far 7. Objects too small 8. Diplopia 9. Excessive Light

10. After Images 11. Monocular and Binocular Vision 12. Displacement of Eyeball

13. Conclusions

1. Introduction

Leonardo devotes considerable attention to optimal and minimal conditions of vision. He emphasizes the importance of the central ray, explores the range of the visual field and considers the problems with objects which are either too near the eye or too small. This leads him to study problems of diplopia. He is aware of the effects of excessive light. In addition he is interested in comparing monocular and binocular vision. Each of these will be considered in turn.

2. Central Ray

Ptolemy, in his Optics¹, stated that objects along the central line of sight are seen more clearly. In Alhazen's Optics² this idea was developed. Witelo adopted it.³ Alberti, in his On Painting goes further:

Leonardo is equally enthusiastic in his praise of this central ray. On A103v (BN 2038 23v, 1492) and again on D8v (1508) he refers it as the master" ray. In an early note on W19148v (fig. 1300, K/P 22v, 1489-1490) he claims that only those objects which are seen along the central line are seen clearly:

(figures)

He returns to this theme on CA138vb (1490):

Of the eye

By way of illustration he gives a concrete example (fig. 1302):

On CA270rb (c. 1490) he again mentions the importance of the central ray in a discussion of the visual process (see above pp. ). On CA144vb (c. 1490) he expresses its importance in more general terms: "the centre is the most powerful and noble part of spherical bodies, because to this respond equally all the extremities of bodies." On A78 (1482) he notes its importance once again: "That object is seen better than the others which falls under a straight line on the middle of each eye under equal angles. On H2 33r (1494) he restates this idea: "No surface will show itself as perfect if the eye regarding this is not equally distant from its extremities." This principle is implicit also in diagrams on CA120rb (fig. 1298, 1497-1498) and CA37rb (figs. 1293-1294, 1497-1498). On CA85v (c. 1503-1504) he illustrates this anew (fig. 1299) now adding a fuller explanation:

As evidence he cites the example of individual letters in a text which can only be discerned clearly when seen along this central line (see A108r, BN 2038 28r, 1492 above pp. ). He pursues this problem on W19152r (K/P 118r, 1508-1510) under the heading:

Of the central line of the eye.

This he illustrates with a diagram (fig. 1300), beneath which he mentions the objection of an adversary:

This claim he refutes (see above pp. ). On D8v (1508) he pursues his discussion of the central ray (fig. 1317, cf. figs. 1314-1316):

A draft passage follows:

In what way the species of objects come to the eye.

Here he breaks off and begins afresh:

These drafts on D8v are closely related to a more polished version on W19117r (K/P 115r, 1508-1510):

He considers the central ray as an example of a more general physical law as he notes on D1r:

Why nature did not make.../the/ power...in the visual power equal.

For Leonardo the central ray is, therefore, another manifestation of his concept of the four powers (see above pp. ).

3. The Visual Field

Euclid, in his Optics, did not attempt to measure quantitatively the limits of the visual field. According to Damianus it was Ptolemy who introduced a proof that the maximal visual cone was ninety degrees.⁴ In the latter Middle Ages this idea was modified slightly. Witelo, for example, claimed, that the maximal visual angle is "nearly a right angle."⁵ Pecham⁶ and Bacon⁷ make the same claim. Leonardo is aware of this traditional claim and attacks it through an appeal to experience on CA204rv (fig. 1307, c. 1490):

On the sight of the eye.

This visual field of 180o, shown in geometrical form on CA204rv (fig. 1307), he illustrates again on CA144vb (fig. 1310, 1490) and CA125ra (fig. 1311, 1490-1492) each time without text.

He subsequently revises his claim. On I46r (fig. 1312, 1497-1499) he indicates a visual field of approximately 240o. This he redraws without explanation on W19117r (K/P 115r, figs. 1318-1321, 1508-1510) and again on W19152r (K/P 118r, figs. 1322-1323, 1508-1510) where he adds: "That which sees the cornea of the eye is seen by this cornea and that which the cornea sees is seen by this pupil. This idea he develops on D8v (fig. 1317, 1508):

It is shown why the eye sees objects in the lateral spaces behind itself

He draws related diagrams on F34r (fig. 1314, 1508) D8r (fig. 1177, 1508) and D3r (fig. 1174). On D1r (figs. 1315-1316), he again adds an explanation:

Why Nature made the pupil convex, that is, raised like part of a ball.

In late sketches on CA385vc (1324-1328, 1513) he indicates a visual field of somewhat less than 180o.

Fiugs. 1324-1328: Sketches concerning the visual field on CA385vc.

Leonardo is also interested in how the eye perceives objects positioned off to the side. On E4r (fig. 1329, 1513-1514), for instance, he broaches this problem under the heading:

Case of perspective

This leads to a conclusion (fig. 1330):

He returns to this problem on G32v (1510-1515) in a passage entitled: “Of this bi-angular figure, the one obtuse angle will be greater than the other to the extent that the eye is closer to the one than the other.” This he illustrates with a diagram (fig. 1331) and then explains:

4. Occlusions

On four folios Leonardo examines how small apertures and their occlusions affect the visual field and perception.⁸ On CA347va (c. 1490), for instance, he begins with a case of two eyes in front of a small hole (fig. 1332): “With straight lines, with an aperture smaller than the sides of the visual pyramid it is impossible to comprehend the object positioned beyond this aperture clearly with the eye.”

He next considers a case (fig. 1333) where one eye is off to the side relative to the aperture:

Eye

In the left-hand column of CA347va he examines a case (fig. 1334) where two eyes can see clearly in spite of occluding objects:

Function of the Eye

Directly below he considers a case (fig. 1335) where an object smaller than the distance between the eyes can, nonetheless, occlude the visual pyramid:

On the eye

Let rca be the visual pyramid. Let df be the place.

Next he considers a case (fig. 1336) where an interposed body occludes vision from one eye:

Eye

The experiment to which he alludes in the last sentence he later describes more carefully on W19042r (K/P 45r, c. 1508) in connection with his studies on light intensity (see below p. ).

In the right-hand column on CA347va he also drafts two further diagrams: one showing how binocular vision remains unaffected when looking through a larger aperture (fig. 1337); a second demonstrating how a small aperture interferes with binocular vision (fig. 1338). Accompanying this latter diagram is a brief text:

On CA347ra he pursues this theme, beginning with a case where a large aperture does not interfere with binocular vision (fig. 1339):

On the Eye

Directly following he describes a situation (fig. 1340) where the aperture is smaller and occludes vision:

On the Eye

This he illustrates with a concrete example (fig. 1340, cf. fig. 1338):

He also draws a third diagram (fig. 1341) which he does not explain. At least fifteen years pass before he returns to the problem in terms of two further diagrams (figs. 1342-1343) without text on CA112ra (c. 1505-1508). On D9r (1508) he pursues this theme, now exploring in detail how a small aperture affects the visual field (fig. 1344):

What part of the background the eyes see looking through a /small/ aperture.

He then considers a situation where the aperture is smaller (fig. 1345):

Where the two eyes will not see a background entirely freely through a given aperture

This leads to an interjection concerning light intensity:

Immediately following he considers the deceptions of sight arising from this situation:

In the next paragraph that follows he relates this deception to that of a style which appears to move in a contrary direction (see above pp. ). In Leonardo's approach one problem continually has cross-references to other problems.

5. Objects too Near

Aristotle had noted that objects touching the eye could not be seen.⁹ Alhazen¹⁰ and Witelo¹¹ repeated this claim. Biagio Pelacani da Parma adds that objects too near the eye are seen unclearly whereas those at a moderate distance are seen distinctly.¹² Leonardo's interest in minimal conditions of vision leads him to consider this problem in greater detail. Among his earliest remarks on the problem in a passage on W19148v (K/P 22v, 1487-1490):

On CA138vb (c. 1490) he estimates the distance for accurate vision:

He offers a slightly different estimate of this minimum distance on CA250rb (c. 1490):

Why this should be so begins to concern him as is evident from a draft passage on CA298va (fig. 1402, c. 1490):

Why this happens more from nearby than from afar

A preliminary explanation follows on CA144vb (c. 1490):

Intimately connected with this problem why nearby objects cannot be seen clearly, are a series of experiments which are also intended to demonstrate that images are spread throughout the pupil and have already been analysed in this connection (see above pp. ). One set of these experiments on D6v (figs. 1346-1349, 1508) involves sieves made of horse hairs. Another series involves pinhole images and styles which are moved back and forth (figs. 1350-1362). A variant of these experiments occurs on F31r (figs. 1363-1364, 1508):

Here the folio ends and the text continues on F30v:

background. Whence it follows that the part g is has little shade (p) because the summit of the object p occludes the view of such a site from the part f of the eye. But it does not follows, however, that the entire remainder of such a pupil does not see this site g, but in h it iwll appear more obscure because its smaller part of the pupil sees it than at g, and lwss of the pupil sees i and less /of the pupil sees/ k and the entire height of such a pupil goes on consuming itself successively in this sight, through which the object p darkens its background at each degree to such an extent that in the end the entire colour of such an object remains wholly obscured.

He returns to these themes on D10v (1508) in a passage entitled:

How the eye does not recognize the boundaries of any body.

Here the folio ends and the text continues on F30v (fig. 1364):

He returns to these themes on D10v (1508):

How the eye does not recognize the boundaries of any body.

is noted

Immediately following he offers a concrete example

He ***???

Immediately following he offers a concrete example (fig. 1365):

He adds a marginal note concerning the boundaries of paintings:

There follows what was lacking below.

A passage in Melzi's hand on BM Arundel 188r (figs. 1368-1369, cf. 1367, c. 1510) summarizes Leonardo's findings concerning the unclear boundaries of nearby objects:

On E15r (1513-1514) Leonardo takes up this theme once more (fig. 1366):

On E15v, cited earlier (see above p. ) the connection is again evident between his demonstrations that images are all in all the pupil and his claim that nearby objects are not seen clearly.

Related to the foregoing series of demonstrations involving an interposed stick are three further examples in the Treatise of Painting involving an interposed sphere positioned close to the eye. One of these on CU805 (TPL742, 1508-1510) simply makes the point that different parts of the pupil see opaque objects differently (fig. 1370):

On CU806 (TPL741, 1508-1510) he relates this demonstration both to the claim that nearby boundaries are unclear and to the principle that the visual power is everywhere in the eye (fig. 1371):

In a third example on CU808 (TPL743, 1508-1510) he again uses the same basic demonstration, this time to emphasize the confused boundaries of nearby obejcts (fig. 1372):

How that body has its boundaries more confused which is closer to the eye that sees it.

6. Objects Too Far

In the case of objects too far from the eye, Leonardo explores further problems of perception. Concerning objects in shade, for instance, there is draft, possibly in another hand on BM Arundel 101r (1490-1495): “Many umbrous bodies very close to one another, being seen in the luminous air at a long distance appear separated by a long interval.”This idea he restates clearly on C144 (1490-1491): “If many umbrous bodies very close to one another are seen against a luminous backgrouind, at a long distance they appear separated by a large interval.”

The converse, that luminous bodies tend to merge at a large distance, is expressed in a draft, again possibly in another hand, on BM Arundel 101r

Many luminous bodies very close to one another, the distant lights appear to the eye to be united and attached together.

He restates this on C14v (1490): "If many luminous bodies are seen from afar, even though they are separated from one another they will appear united and conjoined together." Elsewhere in the same manuscript on C6r (fig. 1373, 1490) he describes a related phenomenon, how a luminous object seen from afar appears larger:

On A64v (1492) he integrates his description of both of these phenomena in a:

Proof how luminous bodies appear larger than they are from a distance.

On Forst. III 35v (1493) he cites the case of a sieve which appears without apertures at a distance. As will be seen below this case is equally relevant with respect to objects which are too small. This paradox that light sources appear to increase in size with distance has a special bearing on his astronomical interests. He suspects that the apparent size of stars might be affected by optical illusions, and therefore explores the problem in detail in the Manuscript F (see below pp. ).

7. Objects Too Small

The minimal size of objects which can be seen clearly was a well established problem in the optical tradition. It had been broached by Galen¹³ and discussed by Alhazen¹⁴, Witelo¹⁵, Biagio Pelacani da Parma¹⁶ and the anonymous author of Della prospettiva¹⁷. Perhaps the earliest of Leonardo's extant notes on this problem occurs on C27r (c. 1490-1491) beginning with a general statement:

To support this he cites the example of a sieve:

He cites this example again on Forst III 35v (c. 1493): “A seive through which the luminous air penetrates, at a long distance will appear without apertures and entirely luminous.” On C19v (1490-1491) he studies the nature of this occlusion or non-occlusion of nearby objects in detail (fig. 1377 cf. fig. 1379):

Immediately following he adds a further note:

As for objects larger than this minimal size, he points out, on C10r (1490-1491):

This problem of the occlusion of nearby objects becomes intimately connected with Leonardo's theories concerning the visual process. His reasoning is as follows: if vision occured through images converging to a point then a small object near the eye would occlude everything behind it. If small objects do not produce occlusion then images must be inverted at the pupil and the visual power must be "all in all and all in every part." As early as 1490 he alludes to this connection between the perception of small objects and the nature of the visual process in a draft passage on CA298va (fig. ):

On CA290rb (c. 1490) he pursues this problem with two detailed diagrams (figs. ) one without text, the other with the accompanying passage:

This problem of the occlusion of nearby objects becomes intimately connected with Leonardo's theories concerning the visual process. His reasoning is as follows: if vision occured through images converging to a point then a small object near the eye would occlude everything behind it. If small objects do not produce occlusion then images must be inverted at the pupil and the visual power must be "all in all and all in every part." As early as 1490 he alludes to this connection between the perception of small objects and the nature of the visual process in a draft passage on CA144vb (fig. 1305):

He explores the problem of objects smaller than the eye in a series of sketches (figs. 1381-1387) and a text on CA298va (1490):

Why the object near the eye leaves its boiundaries indiscernible.

To complete the explanation he appeals to his concept of the central ray (see above p. ):

On CA290rb (1490) he pursues this problems with two detailed diagrams (figs. 1388-1389) one without, one with text:

On A103v (fig. 1398, BN 2038 23v, 1492) he provides another explanation:

On A77 (figs. 1399, 1492) he analyses this problem in connection with his demonstrations that vision does not occur at a point. Here a connection between his notion that images are "all in all and all in every part of the pupil" remains implicit. In subsequent passages on BM112r and CA250va (see above pp. ) he develops these connections between (a) his theory that images do not terminate at a point in the eye and b) problems of perception of objects smaller than the eye. By 1500 on CA237ra he draws two diagrams of the eye looking at objects smaller than the pupil (figs. 1404-1405) and merely adds alongside:

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

Here he takes for granted the connection between his theory of vision in terms of images being "all in all..." the eye and the perception of objects smaller than the eye. On CA112ra (1506-1508) he alludes to this connection in two diagrams without text (figs. ). By 1508 the connection is explicit. Hence his experiments involving horse-hairs (figs. 1346-1349) and styles (figs. 1350-1362) close to the eye are used a) to refute the print theory of vision (see above pp. ) and b) to explain why the eye cannot see nearby objects clearly. In Leonardo's associative mind there is also a connection between the quantity seen of nearby objects (see above pp. ) and the quality with which they are seen due to occlusion. This connection is implicit in a passage on Forst III 36r (figs. 1400-1401, cf. 1402-1403, c. 1493):

Which object is better seen.

On K125/45/r (figs. 1412-1413, after 1504) this connection becomes more explicit:

On K124/44v/ (figs. 1410-1411) he pursues the question of the quantity of objects seen (see above pp. ). In 1508 he returns to the theme of occlusion on F28v (figs. 1379-1380, cf. figs. 1377-1378):

Which demonstration leads to a further attack on the point theory of vision (fig. 1377; see above pp. ):

On D9r (fig. 1356, 1508) he again considers the transparency of objects smaller than the pupil:

Leonardo also relates these problems of occlusion in the case of objects smaller than the eye to both his study of linear perspective and the camera obscura, as is evidenced by an early passage on A65 (fig. 1414, 1492):

On H71/23/r (1493) he again relates this problem of nearby objects to his camera obscura studies (see above p. ) when he notes that (fig. 790): "the eye does not comprehend the nearby luminous angle."

Objects smaller than the distance between two eyes

Euclid, in his Optics had broached the question of how much is seen of objects smaller than the distance between the eyes. Leonardo also examines such questions (see above pp. ) but in addition explores perceptual problems not considered by Euclid. On W12351r (c. 1493-149 ), for instance, he discovers that objects smaller than the distance between the two eyes contradict a basic law of linear perspective wehreby projected size varies inversely with distance (fig. 1415):

On CA120vd (c. 1504) he draws a similar situation (fig. 1416) except that the rectangular figure is seen from the side. No text accompanies this draft. On CU804 (TPL821, 1505-1510) he explains the phenomenon:

Of Perspective

This he illustrates with an example (fig. 1417):

Meanwhile he had also been studying what effects of occlusion occur with sucj objects smaller than the distance between the two eyes. On C23r (1490-1491), for instance, he notes:

This he illustrates (fig. 1419, cf. fig. 1418) and then describes:

Let r /and/ s be the eyes that look at the above mentioned object.

In this example only the space ab is occluded from both eyes. Directly beneath this he draws a second example (fig. 1420) in which the object is smaller still and consequently occludes none of the background. No text accompanies this diagram. Some two years later he returns to this problem on BM115r (fig. c. 1492):

He then restates the principle in more general terms: “No object situated behind an object seen by the eye can be occluded by this /first/ object if it is less than the space that stands between the pupils.” Leonardo qualifies this general claim in a note on CA347va (earlier 1490-1495):

This he again illustrates with an example (fig. 1335):

Further consideration of the problem leads him to claim, on CA250rb (c. 1490) that if objects smaller than the interval between the two eyes are to be seen clearly, a minimum distance four times that between the two eyes is required (fig. , see above p. ). On CA175ra (c. 1493-1494) he pursues this theme under the heading (figs. 1421-1422, 1424-1428, cf. figs. 1418-1420):

It is impossible that the opaque body appears of that perfect rotundity as the plane circle.

To explain this phenomenon he again appeals to his concept of the central ray (see above pp. );

He describes a related phenomenon on I43r (fig. 1423, c. 1497-1499):

8. Diplopia

Ptolemy, in his Optics¹⁸, had explored the problem of diplopia in some detail. Some of these experiments were recorded by Alhazen¹⁹. Witelo²⁰ included additional cases in his compilation. Two of Witelo's examples have a parallel in Leonardo's notes (figs. 1430, 1438, cf. figs. 1431, 1439-1444). There is no firm evidence, however, that Leonardo drew directly on these mediaeval sources. His observations concerning diplopia may well have developed from his own detailed studies of objects smaller than the eye. An early example of this problem how a single object can appear double occurs on CA396rb (c. 1492) when Leonardo notes (fig. 1431): "it appears to be 2 because the pyramids do not intersect at it as at a /and/ o. On C19v (fig. 1432, 1490-1491) and CA190vb (fig. 1433, c. 1508) he draws related diagrams without text.

On CA125rb (c. 1490-1492) he draws two eyes with two objects in front of them: one object is seen normally; the other, double (fig. 1434):

This phenomenon he indicates again in a diagram on A2v (fig. 1435, 1492) and a rough sketch on W19096v (K/P 34r, fig. 1436, c. 1493) both without text. Some fifteen years later he analyses the problem in greater detail on D8v (fig. 1437, 1508):

The function of the central lines in the concourse of the visible.

In the foregoing examples one object is positioned flush with the wall or interposed plane and the object which is seen double is nearer the eyes. In another series (fig. 1438) both objects are positioned away from the wall. He draws preliminary sketches of this situation on CA125rb (figs. 1440-1441, c. 1490-1492) and C19v (fig. 1439, 1490-1491). These he develops on W19117r (figs. 1442-1444, K/P 1125r, 1508-1510) accompanying which he explains:

On W19147v (K/P 22v, 1489-1490) he considers a situation in which two eyes have three objects in front of them two of which are doubled, (fig. 1451). This puzzles him. Hence he asks: "why in two /eyes/ or in front of two eyes /when/ three objects are represented 2 /of them/ are /doubled/. He redraws this diagram on A2r (fig. 1452, 1492) this time adding only the captions "distinct" for the single image and "indistinct" for the double image.

On A2r (fig. 1453, 1492) he also draws a smaller diagram illustrating that each of the three objects in turn can appear double depending on where the eye is focussed. This composite diagram he also presents in three separate diagrams on CA125vb (figs. 1448-1450, c. 1490-1492). In a first example (fig. 1448) the eyes focus on the furthest of the three objects and the two nearest objects are both doubled. In a second instance the eyes focus on the middle object (fig. 1449) as a result of which both the nearest and the furthest object appear doubled. In a third case (fig. 1450) the eyes focus on the nearest object, whence both the middle and the furthest object appear doubled. Some fifteen years after he returns to this theme in a diagram (fig. 1454) on W19117r (K/P 115r, 1508-1510) again showing two eyes, now marked a and b in front of three objects c, d, and e respectively. The nearest object c appears double when the eye focusses alternatively on d or e.

On CA347ra (c. 1490) he considers another alternative (fig. 1446), namely, how two eyes a and b, focussed on the point m, perceive the two objects c and d as the four objects e, f, g and h respectively. On C19v (1490-1491) he redraws this diagram, using identical letters (fig. 1447). He also draws a related situation (fig. 1445) in which the objects in front of the eye are somewhat larger. In this case the two objects r and s are perceived as three, namely, t, n and u. These studies lead him, on W19117r (K/P 115r, 1508-1510), to propose an explanation and a general rule concerning the number of apparent images seen in any situation (fig. 1455):

9. Excessive Light

The phenomenon that a greater light overcomes and disperses a lesser one had been considered by Aristotle²¹. Galen mentions it in an optical context in De usu partium.²² In the Arabic tradition Alhazen²³ discussed the problem, whence it was subsequently noted by authors such as Pecham.²⁴ Leonardo alludes to this problem in passing on A100r (BN 2038 20r, 1492): "on the eye which through a greater light cannot discern the lesser ones." This idea he restates in a draft on BM171v (fig. 1456, c. 1492): "When the eye...has luminous objects (in front of it/,..., opaque objects appear tenebrous." He broaches the matter again on F57r (1508) in answering claims that the stars have light of their own:

On CU692 (TPL626, 1508-1510) he describes more clearly this phenomenon:

Of light which converts itself into shade.

A converse experience is described on CU693 (TPL625, 1508-1510);

Of the shade which is converted into light.

Excessive brightness hurts the eye

That excessive brightness hurts the eye was mentioned by Aristotle²⁵ and subsequent authors in the optical tradition including Galen²⁶, Alhazen²⁷, Witelo²⁸ and Pecham.²⁹ Leonardo discusses this problem in connection with variations in pupil size on C15r (1490-1491, see above pp. ). He mentions the problem again on Mad II 23v (1503-1504), this time in connection with background illusions involving glowing irons (see above p. ):

On D7r (1508) he returns to this theme in connection with varying pupil size:

10. After Images

This visual phenomenon can be traced back clearly to Aristotle's De somniis.³⁰ Ptolemy discusses the problem in his Optics³¹ as do later authors such as Witelo³² and the anonymous author of Della prospettiva³³. Leonardo's earliest extant reference to after-images occurs on Triv. 43r (1487-1490) in connection with the four powers:

Concerning violence

To support this general claim he cites examples from acoustics and optics:

Example.

On C7v (1490-1491) he seeks to explain after-images in terms of a principle of opposites:

He returns to this explanation on CA203ra (1489-1490):

On CA204va (c. 1490) he mentions the phenomenon anew: "The eye reserves within it the images of luminous things which represent themselves to it," and on CA204ra he cites such after-images as evidence to support the intromission theory of vision (see above pp. ):

Proof how objects come to the eye.

A more vivid description of the consequences of looking at the sun follows on CA369vd (c. 1490): “The dark place is seen inseminated with luminous round spots and the luminous /place/ with dark /round spots/ by the eye which many times and quickly has just look at at the body of the sun.” On CA250va (c. 1490) he offers a rule concerning the duration of these after-images: "Those images which are born from a more luminous body will be reserved in the eye to a greater extent." Nearly eighteen years later he uses this phenomenon to explain the characteristics of the crystalline lens on D5v (1508):

Whether the eye sees bright and dark things at the same time?

He mentions the problem once more on G73r (c. 1513), where, having provided various definitions of impetus, he adds:

Every impression tends to permanence or desires permanence.

He had used the same examples in his earliest extant note on after-images on Triv. 43r (147-1490). To illustrate the phenomenon of after-images Mediaeval optical writers such as Biagio Pelacani da parma and the anonymous author of Della prospettiva had also cited the instance of a firebrand which, when revolved, appeared to be a flaming circle.³⁴ Leonardo adapts this example on A26 (1492) in a passage entitled:

Perspective and motion

Every body which moves with speed, appears to tinge its path with the image of its colour.

He pursues this theme in the Manuscript K (post 1504) where he establishes that this phenomenon is dependent on two factors rapid movement (a) of the eye and (b) of the object. He discusses the first of these on K120/40/r (fig. 1263) under the heading:

On K119/39/v, he considers a second faxtor: movement of the object:

He develops his ideas on the forebrand on CA207ra (1508-1510) in the form of claims:

If the motion of this fire and the air which occludes it is uniform then such fire will remain without a tail.

This stick illustrates in two sketches (figs. 1457-1458) adding the captions:

Let a be the stick, b the wind, uc the tail of fire.

On the W19117r (K/P 115r) he cites another example of after images:

This illustration of after-images is alluded to again on G6v (1510-1515) under the heading. "Description of the flood" where he refers to "the lines which drops of water make in descending" and once more on CA79rc (1515-1516): “The stone thrown through the air leaves in the eye that sees it the impression of its motion and the drops of water which descend from the clouds when it rains, do the same.” Meanwhile, he had cited all three of these illustrations of after-images: namely, the sun's image, the waving firebrand and the apparent lines of rain, on CA360ra (c. 1504) opening, as usual with a general statement:

After giving examples from acoustics, he turns to after-images in vision:

11. Monocular and Binocular

Leonardo examines how monocular and binocular vision affect the apparent brightness, clarity and relief of objects. With respect to brightness, for instance, he notes on H91/43/v (c. 1494) that "the luminous body appears larger and more luminous with two eyes than with one." On Mad II 24r (1503-1505) he develops this idea:

This claim he reformulates, now adding an example

On Mad II 25v he restates this idea (fig. 1461):

Beneath the diagram (fig. 1461) showing a human imprensiva, he adds the caption "a is the imprensiva for seeing luminous objects." He describes a related experiment on W19042r (K/P 45r, fig. 1462, c. 1508):

These demonstrations recall those in which he studies the effects of various sizes of pupils (see above pp. ). Aristotle, in the Problemata³⁵ had noted that objects seen by two eyes are seen more clearly than with one eye. Ptolemy³⁶ amd Witelo³⁷ also mention this. Leonardo refers to this implicitly on several occasions and explicitly on CA347ra (1490) under the heading:

Of the eye

The way in which binocular vision contributes to effects of relief interests him far more because it raises the question whether a painting achieved with a monocular vanishing-point can ever fully imitate the perceptual effects of objects seen with two eyes. His notes on this problem have been analysed elsewhere (see above vol. 1, part III, 4). As noted in the introduction (see above p. ) this particular aspect of his interest in binocular vision served in 1839 as a starting point for Wheatstone's classic essay on the stereoscope.

12. Displacement of Eyeball

Abnormalities of sight and the pathology of vision constitute a domain to which Leonardo devotes very little attention in the extant notes. An exception is the displacement of the eyeball. The phenomenon as such was well known. Aristotle, for instance, had considered it in his Metaphysics.³⁸ Leonardo's first extant reference to this problem is in the form of a brief question on CA125rb (c. 1490-1492): "Why the eye, pushed by a finger, sees itself, which appears, /as/ a circle of fire." On BM115v (figs. 1468-1469, c. 1492) he broaches the problem again:

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

These notes on BM115v may well have been a draft for a passage on A81r (fig. 1467, 1492) where he discusses this problem in greater detail:

On CA204rb (c. 1490) he cites this as the most important demonstration to confirm the intromission theory of vision (see above p. ). In the late period he returns once more to this phenomenon on W19117r (K/P 115r, figs. 1470-1473, 1508-1510):

The image.

To illustrate this he drafts a rough diagram (fig. 1470) which he crosses out and draws again (fig. 1471) showing in composite fashion both the central rays rt and st and the non-central lines sx and sv. Next he draws a sketch showing only the central lines (fig. 1472) and a further sketch with the two central lines and one of the non-central lines (fig. 1473). These final two diagrams he does not discuss in his text.

13. Conclusion

Euclid had focussed on ordinary visual conditions in his Optics. In the mediaeval period authors such as Alhazen, Witelo, Pecham and Biagio Pelacani da Parma had devoted more attention to problem conditions of vision. Leonardo develops these interests. He devotes attention to the role of the central ray, but is equally concerned with determining the limits of the visual field. His experiments in this connection lead him to reject the mediaeval notion that the maximal viewing angle is 90 degrees. Further experiments in this connection involve the use of occlusions and small apertures. He does not, however, perform Scheiner's experiment.

Leonardo writes extensively on the perceptual problem of objects too near the eye, too far from the eye and too small to be seen clearly. He develops models and demonstrations for these purposes. He also studies diplopia and develops a rule for the number of images seen. The problem of excessive light he considers briefly. The question of after-images concerns him more. He has some notes on the distinction between monocular and binocular vision. Displacement of the eyeball also concerns him because he believes that it offers conclusive evidence for the intromission theory of vision. Notably absent from his writings are studies of pathological conditions of vision. Even fairly common disorders such as squinting or cataract are not mentioned in his extant work.

Notes

1. Optics - Ptolemy ↩︎
2. Alhazen's Optics ↩︎
3. Witelo ↩︎
4. Damianus ↩︎
5. Witelo ↩︎
6. Pecham ↩︎
7. Bacon ↩︎
8. Leonardo ↩︎
9. Aristotle ↩︎
10. Alhazen ↩︎
11. Witelo ↩︎
12. Biagio Pelacani da Parma ↩︎
13. Galen ↩︎
14. Alhazen ↩︎
15. Witelo ↩︎
16. Biagio Pelacani da Parma ↩︎
17. Della prospettiva ↩︎
18. Ptolemy - Optics ↩︎
19. Alhazen ↩︎
20. Witelo ↩︎
21. Aristotle ↩︎
22. Galen - De usu partium ↩︎
23. Alhazen ↩︎
24. Pecham ↩︎
25. Aristotle ↩︎
26. Galen ↩︎
27. Alhazen ↩︎
28. Witelo ↩︎
29. Pecham ↩︎
30. Aristotle's De somniis ↩︎
31. Optics ↩︎
32. Witelo ↩︎
33. Della prospettiva ↩︎
34. Della prospettiva & Biagio Pelacani da parma ↩︎
35. Aristotle - Problemata ↩︎
36. Aristotle, in the Problemata ↩︎
37. Witelo ↩︎
38. Aristotle - Metaphysics ↩︎