Part Two, Chapter 3: The Camera Obscura

1. Introduction 2. Astronomical Context 3. Inversion of Images 4. Non-interference

5. Images all in all 6. Intensity of Light and Shade or Image 7. Contrary Motion

8. Size of Aperture 9. Shape of Aperture 10. Number of Apertures 11. Apertures and Interposed Bodies 12. Spectrum of Boundaries 13. Camera Obscuras and the Eye

14. Conclusions

1. Introduction

Leonardo has commonly been credited with the invention of the camera obscura¹. This is not true. Unequivocal descriptions of the instrument go back at least until the ninth century AD² and by the thirteenth century it had assumed an important function in astronomy.³ On the fourth of June, 1285, for instance, William of St. Cloud used a camera obscura to observe an eclipse of the sun.⁴ This use of the camera obscura develops in the fourteenth century and in the latter fifteenth century provides one source of Leonardo's interest in the instrument. He uses it, for example, to estimate the size and distance of the sun and moon.

The aperture of the camera obscura is, for Leonardo, analogous to the aperture of the pupil and this leads him to study various characteristics of apertures: how images passing through them are inverted, how they do not interfere with one another, how such images are "all in all and all in every part"; how they can vary their intensity, and how they move in a contrary direction beyond the aperture. He considers the effect of changing the size of the aperture and examines in some detail both the properties of a single aperture with a changing number of sides and the characteristics of multiple pinhole images. From a note on CA277va (1513-1514) cited above (see p. ), he clearly intended to adopt these findings for two additional books on light and shade.

Indeed many of the experiments that he had made with umbrous bodies in the open he repeats in combination with a camera obscura, now focussing on a particular phenomenon: how the boundaries between light and shade are actually a series of subtle graduations. These late studies of 1508-1510, as will be shown, have important consequences for his theories of vision and perception. But before considering these, we need to examine the details of his camera obscura studies.

2. Astronomical Context.

Leonardo's earliest extant reference to the use of an aperture in observing eclipses is on Triv.6v (fig. 678, 1487-1490):

In this case the image is seen directly and the aperture serves merely to screen off excessive light. On CA270vb (c. 1490) he describes a case where the image is seen indirectly under the heading:

How bodies...send...their form and heat and power beyond themselves.

Immediately following he offers a (cf. fig. 679).

Second example.

Finally he provides an illustration that simulates the effects produced by these natural phenomena:

Third example.

CA125vb (fig. 694), and CU789 (fig. 704). The case of the moon is also considered on A64v (1492):

On A61v (1492) he pursues this theme, now adding an illustration (fig. ):

The problem of the moon's shape continues to perplex him. On CA243ra (1510-1515) he notes:

The use of the camera obscura in determining the diameter of the sun had been discussed by late mediaeval authors such as Levi ben Gerson⁵ (c.1370). This also interests Leonardo as is shown by a diagram on A20v (fig. 679, cf. A21r, fig. 680 and Mario Bettini, fig. 681) beneath which he adds:

The problem is not forgotten. On CA225rb (1497-1500) he reminds himself in passing of "the measurement of the sun promised me by Master Giovanni the Frenchman." On BM174v (1500-1505) Leonardo describes a more complex procedure involving a combination of camera obscura and mirror (fig. 682):

The precise function of this procedure is not explained.

On Leicester 1r (1506-1509) he alludes to but again does not elaborate on a:

To this problem of sizes and distances of the planets he returns on CA243rb (1510-1515) now providing a more detailed explanation:

The method here described is identical to the surveying procedure used to demonstrate principles of linear perspective on CA42rc, (cf. vol. 1, fig. 122). On CA151va (1500-1506) he gives an alternative method of measuring the distance of the sun, this time using a staff again familiar from the surveying tradition. Lower down on CA243rb he draws a rough sketch of a camera obscura (fig. 683) beneath which he notes "Measure of the size of the sun, knowing the distance." On CA297va (1497-1500) he drafts a passage concerning the use of apertures in a meteorological context:

This he drafts again directly below:

These drafts serve in turn as the basis for a passage on CU476 (fig. 684, TPL447, 1510-1515):

On the solar rays that penetrate the apertures of clouds.

Also in this late period, on CA248va (fig. 685, 1510-1515), he again mentions the relative intensity of the sun's illuminating in a camera obscura:

These astronomical and meteorological uses of the camera obscura constitute but a small part of Leonardo's concern for this instrument. He is fascinated by the analogies that it offers with the pupil (see below pp. ) and therefore employs the camera obscura to demonstrate such optical principles as inversion of images, their non-interference, and their existence "all in all and all in every part." We shall examine each of these in turn.

3. Inversion of Images

Leonardo believes that images are inverted in passing through the aperture of the pupil. As early as 1489-1490 he employs a camera obscura to demonstrate this principle in a passage on W19147v (K/P 22v):

A specific example follows (fig. 686):

He pursues this eye-camera obscura analogy on C6r (fig. 688, 1490-1491):

He illustrates this inversion principle in sketches without text on Forst III 29v (fig. 869, 1490-1493), CA155rde (fig. 692, 1495-1497) and BM170v (fig. 692, 1492); then mentions it again on BM232v (1490-1495):

A further illustration occurs on CA125vb (fig. 694, 1492) accompanying which he drafts an explanation:

On CA126ra (c. 1492) the problem is further illustrated (fig. 156). Thereafter, more than a decade passes before he broaches the problem again on CA345vb (figs. 695-696, 1505-1508):

In the Manuscript D he discusses the problem of inversion at length. A first passage on D10r (c. 1508) is entitled:

Of the species of objects that pass through narrow apertures into a dark place.

To demonstrate this he provides a concrete example (fig. 697):

On D8r he pursues this analogy between eye and camera obscura under the heading:

How the species of objects received by the eye intersect inside the albugineous humour.

A concrete demonstration follows (fig. 698):

He again mentions this way in which images are inverted in passing on W19150v (K/P 118v(a), fig. 699, 1508-1510): "No image of however small a body penetrates the eye without being turned upside down....." On CA241vc (also 1508-1510) he produces two further drafts:

These he crosses out and reformulates:

4. Non-Interference

The non-interference of images is another phenomenon which he demonstrates using the camera obscura. On A93r (BN2038 13r, 1492), for instance, he shows how a red, white and yellow light can intersect without interference (fig. 700). Similar demonstrations occur on CA256rc (figs. 701-702, c.1492) involving a red, green and yellow light and a red, white and green light. Accompanying these are a series of draft notes concerning the intensity of colour, light and shade passing through apertures:

The qualities of rays are 2, that is: luminous and umbrous.

On 19112r (K/P 118r, 1508-1510) he returns to the theme of non-interference of colours in a camera obscura, this time using yellow and blue lights (fig. 703). Slightly more complex is a demonstration on CU789 (fig. 704, TPL707, 1508-1510) where he shows how light from a candle and from the air produces different colours on an interposed object:

Of the colours of lights illuminating umbrous bodies.

On CU797 (TPL645, 1508-1510) he had used a similar demonstration to establish that the colour of shadows participates with the colour of surrounding objects (see above pp. ). On W19150v (fig. 705, K/P 118v, 1508-1510) he pursues both the themes of colour participating and non-interference of images under the heading:

Of the rays which carry the images of bodies through the air.

On the recto of this same folio (K/P 118r) this phenomenon of the non-interference of images is discussed further in a passage entitled:

(figures)

This claim he qualifies:

5. Images All in All

The way in which Leonardo uses a camera obscura to establish that images are all in all and all in every part has been analysed previously (see above pp. ). This was chiefly in terms of passages on A9v (fig. 133, 1492) and W19150v (figs. 706-706, K/P 118v, 1508-1510). This principle is also implicit in a sketch on BM171r (fig. 708, 1492) beneath which he writes:

It is equally implicit in other sketches on W12352v (fig. 709, 1494), CA91vb (fig. 710, C.1500), CA112va (fig. 711, 1505-1508), as well as in a series of sketches (figs. 712-726) on CA238rb, vb (1505-1508) accompanying which is only an interrupted text: “Every part of ab...is in every part...d, but more...illuminate...short ray...where the spe/cies.../ powerful occupy...the less powerful.” On CA155rd (figs. 729-732, 1497-1500) he implicitly demonstrates this principles again in a series of four diagrams accompanying which he merely notes:

abfik is according the adversary; abcgh is mine.

This principle is illustrated roughly once more in a diagram without text on W12353 (fig. 734, 1508-1511).

6. Intensity of Light and Shade or Image

Images in the camera obscura may be "all in all and all in every part." Nonetheless, Leonardo is convinced that they can vary in their intensity, and he uses the camera obscura to demonstrate this. On C14v (1490-1491), for instance, he draws a rough diagram (fig. 735) which he then develops (fig. 736). Accompanying this he opens with a general comment:

This is followed by a specific demonstration which refers back to the diagram (fig. 736):

This theme of differing intensities of light within the camera obscura is mentioned in passing on CA256rc (fig. 733, 1492): “The luminous rays make the shadows of bodies greater which are opposite the aperture and the percussion, which bodies are touched by a less luminous ray.” On CA238rb (1505-1508) following the all in all passage cited previously (see above p. ), he again takes up this theme of differing intensities of light and shade (fig. 723):

He now draws a second diagram (fig. 724) which he explains:

Another diagram follows (fig. 726 cf. 727-728) accompanying which he notes: "When the motion is from n to m, the shadow will descend from a to b." On this single folio CA238rb (1505-1508) he has thus used a camera obscura to demonstrate that (1) images are all in all and all in every part (see above pp. ); (2) that images vary in their intensity and (3) that images inside a camera obscura are inverted mind these three demonstrations are closely related. It is no wonder, then, that the remaining preparatory sketches on this folio (figs. 715-719, 722, 725) which are without text have a certain ambiguity about them: they could serve to support any of or all three of these demonstrations.

On C12v (fig. 737, 1490-1491), in the course of his studies of light and shade, he had illustrated how a light source in front of two opaque bodies produces concentric rings of light and shade of different intensity. The text on C12v is closely related to a draft, possibly in another hand on BM101r (1490-1495):

BM101r C12v

That umbrous body of spherical That umbrous body of spherical

rotundity will make circular rotundity will make circular mixed

mixed shade which will be be- shade which has placed between it

tween it /and/ the sun a body and the sun an umbrous body of its

placed opposite it similar to quality.

its quality /and/ quantity.

This demonstration of concentric rings caused by opaque bodies in the open air is the more interesting because it is paralleled by further demonstrations involving camera obscuras. On CA242v (1497-1500), for instance, he draws (fig. 738) sunlight entering through an aperture which is intersected at various distances. Directly beneath he describes the first percussion:

He then describes the second percussion

And the said space ab is seen by op and the space cd by nm which obscure it.

A description of the third percussion is given short schrift: "At the 3rd figure bc is seen by all the body of the sun."

He pursues this theme on CA262ra (1497-1500). Here he carefully redraws his diagram showing various percussions of sunlight within a camera obscura (fig. 739). Directly above this he drafts a general claim: “The solar ray which penetrates inside the apertures (of the eye) of houses, in each degree of its length changes quality as quantity.” It is noteworthy how he here writes "apertures of the eye" which he then crosses out to write "apertures of houses." The correction is significant because on the same folio he also discusses different kinds of pupils (see pp. ). The camera obscura-eye analogy is very important for him. Not content with his first draft he crosses it out and begins afresh: “The solar ray which, through a narrow aperture made in a thin wall, penetrates a dark place, in each degree of its length m...” Here the text breaks off. Beneath the diagram he starts anew, now with a description of the 6th percussion.

He returns to this theme in a sketch without text on CA238rb (fig. 740, 1505-15087). In the Manuscript F similar sketches becoming a starting point for theories of the pupil (figs. ** , see below pp. ** ).

7. Contrary Motion

Leonardo's use of the camera obscura to demonstrate the phenomenon of contrary motion can be traced back to a note on C3r (fig. 741, 1490-1491):

He pursues this theme in a series of sketches without text on CA357rb (figs. 744-748, c. 1490). On CM171v (1492) the principle is again mentioned:

Further sketches (figs. 742-743) without text follow on CA133va (1497-1500). Approximately a decade later he demonstrates this principle of contrary movement of images in a camera obscura by moving the edges of the aperture on W19149r (K/P 118r, figs. 749-751, 1508-1510, see above pp. ). In this same passage he also broaches the themes of aperture size, rectilinear propagation and the principle that images are all in all in every part.

Gis. 752-756: Experiments concerning contrary motion of images in a camera obscura on CA277va.

his approach is experimental and systematic. He begins with a situation (fig. 752-753) where a stick, situated in a high position in front of a near wall, casts a shadow low down on the far wall. The accompanying text is headed:

Operation of compound shade.

The operations of compound shade are always of contrary motion.

Having considered the contrary motion of this stick's shadow when the stick is positioned in front of the first wall (fig. 754), he explores what happens if the stick is positioned behind this first wall:

Next he turns to a case where the stick is positioned in the same plane as the first wall (fig. 755, cf. fig. 756):

This passage ends with a general comment:

He returns to this theme of contrary movement on E2v (1513-1514) in a passage headed:

On shadow and its movement.

This he demonstrates with a concrete example (fig. 757):

8. Size of Aperture

Concerned as he is with studying the variables of a given problem it is not surprising to find him exploring the role played by different sizes of aperture. On CA373rb (1490-1495) he merely makes two preliminary diagrams without text (figs. 758, 762). These he develops in two diagrams (figs. 759, 763) on CA256rc (1492) where he draws a thin and a thick wall alongside which he writes:

On H227 in f. 47v=48r he takes these ideas further. Here he draws a thick wall (fig. 760) accompanying which he notes: "The aperture that is positioned in a thick wall will give little light to the site where it reaches." He also draws a thin wall (fig. 764) with the comment: "That aperture that is positioned in a thinner wall will give more light to the place where it reaches." He pursues this theme on A2r (fig. 761, 1492) where he draws a relatively thin wall and considers changing intensities of light inside a camera obscura under the heading:

Quality of lights

On A85r (BN2038 5r, 1492) he draws a related diagram (fig. 765) alongside which he drafts an explanation:

Not content, he crosses this out and reformulates it under the heading of:

Painting

He redraws the diagrams of A2r and A85r on CA262v (figs. 766-768, 1497-1500) this time with no accompanying text. About a decade later he takes up this theme of apertures of different sizes once more in W19152v (K/P 118v, 1508-1510), beginning with a general claim: “Images which pass through apertures into a dark place intersect their sides that much nearer to the aperture to the extent that this aperture is of lesser width.” By way of illustration he draws three diagrams and first discusses the case (fig. 769) on the far left in which the opaque objects ab and ik produce shadows which pass through the aperture de:

Gis. 769-771: Demonstrations of concerning different sizes of aperture in camera obscuras on W19152v (K/P 118v).

He proceeds to discuss the two figures to the right of this, namely, abc, which is on the far right, (fig. 771) and nmo which is on the near right (fig. 770, or as he puts it, to the left relative to abc):

He then considers further properties of the diagram at the far left (fig. 769):

This discussion of where image formation occurs leads him to mention where images are doubled:

Here the physics of light and shade dovetails with the problem of image formation in a camera obscura which interests him because of its relevance to vision (see below pp. ). In Leonardo's mind one topic constantly leads to another.

These interweaving analogies he develops on CA385vc (1510-1515) where he sketches two examples with two opaque bodies (figs. 772-773) and three cases with three such bodies at various distances (figs. 774-776). Other sketches on the same folio (figs.** ) make explicit the camera obscura-eye analogy and leave no doubt concerning the parallels intended between physics of light and shade and physiology of vision.

9. Shape of the Aperture

When light passes through an aperture does the resulting image on the wall resemble the shape of the aperture or the light source? Already in Antiquity this had been a problem as is evident from two questions posed in the Problemata attributed to Aristotle:

Alhazen, in the eleventh century, had mentioned the problem of light passing through apertures.⁶ Witelo, in the thirteenth century had considered briefly light passing through square, round and angular apertures.⁷ With Pecham this phenomenon emerged as a serious problem. He devoted two of his longest propositions to the properties of images passing through triangular apertures.⁸

Leonardo stands clearly within this tradition. A diagram on A82v (fig. 778, 1492) bears comparison with standard diagram from Pecham's work (fig. 777). But whereas his predecessors had been content to consider isolated cases, Leonardo is more systematic. In his notebooks he illustrates a series of situations showing how, with greater distance, the image gradually loses the shape of the aperture and takes on the shape of the light source. When the light source, aperture and projection plane are very close, the light passing through a triangular aperture produces a triangular image. This limiting case (fig. 783) he considers in some detail a situation in which a triangular image begins to become curved (figs. 780-782, cf. fig. 779):

The exterior sides of compound derived shade are always seen by all the luminous body.

But if the angle is convex then the impression of the obtuse angle will make an acute angle.

(Figs. 783-788: Stages in the transformation of a triangular image to a round image. Fig. 783, Author's reconstruction: fig. 784, CA277va; fig. 785, C10v; fig. 786, Forst III 29v; fig. 787, H227 inf. 50v-51r; fig. 788, H227 inf. 49r.

How the shadow of an obtuse angle makes itself acute with curved sides.

He illustrates this situation on CA277va(fig. 784, 1508-1510). On C10v (1490-1491) he shows (fig. 785) a next step in this process where the circles have begun to overlap. The accompanying text summarizes the phenomenon:

On Forster III 29v (fig. 786, c. 1493) he demonstrates a next stage in this process of transformation. The distance is now greater and the three circles have begun to overlap more. The accompanying text is brief: "The angle is terminated in a point. In the point are intersected the images of bodies." A next stage, where the distance is greater and the circles overlap even more is recorded on Manuscript H 227 inf. 50v-51r (fig. 787) accompanying which is a thorough explanation:

When the distance is greater still the image takes on entirely the shape of the original light source and is fully round, in spite of having passed through a triangular aperture.11 This situation he describes in draft on CA135va(1490-1492) and develops on H227 inf. 49r (fig. 788):

CA135va H227 Inf. 49r

The further from the intersection The further from the intersection

/that/ the second pyramid /is/, ... that the base of the second

the more it expands at the object. pyramid made the object is

Its circles created at the angle generated, the more it expands.

of the aperture enter more into And its circles created in the

the body (the one than the other) angles of the apertures are

and to the extent that they incorporated together more, and

incorporate one another, the more the more that they are incorpora-

the solar ray remains round at ted together, the rounder the

the object. base of the solar pyramid remains.

path that they enter four hundred times

into the greater diameter of the

aperture, the rays will carry to the

object a spherical body and the form

of the aperture will be lost.

Given his interest in the light-sight analogy (see above pp. ) it is not surprising to find him on H71 /23/(r) (fig. 790, 1494) examining what happens when an eye looks through a triangular aperture. "The eye," he concludes, "does not comprehend the nearby luminous object."

He is equally interested in the properties of square apertures and occluding objects. On C12r (1490-1491), for instance, he (fig. 791) asks: "What shadow a square umbrous body will make with a spherical luminous source?" On A20r (1492) he notes how: "the solar rays repercussed on the square mirror will rebound in a circular form on the distant object." On CA256rc(c. 1492) he considers a variant situation in which (fig. 792) a rectangular light source passes through a circular aperture and projects a rectangular image.

When a circular light source, a square aperture and a projection plane are close to one another, the projected image takes on the squareness of the aperture. This limiting case (fig. 793) Leonardo does not illustrate. As the distance increases each of the four corners of the aperture generates intersecting circles. This situation he illustrates (figs. 794-797) and describes at length in a passage recorded on H227v inf., 48r-48v:

The passage ends with a description of what happens when the distance is increased:

How these circles gradually come together as the distance increases he sketches roughly on CA135va (fig. 798, 1492), and then with more care in a diagram recorded on H227 inf. 48v (figs. 799-800) accompanying which he writes:

Proof in what way the square is made in the form of a sphere by the solar rays at the object.

This description of how a square is transformed into a circle effectively provides a visual demonstration of the age old problem of quadrature of the circle. Which raises the question: did Leonardo perhaps see in these optical experiments a case study in principles of practical geometry? This would, for example, account for a striking resemblance between the diagrams (figs. 795-795) just analysed and a diagram on Forst II 5v (fig. 794, c. 1495-1497), above which he writes "True proof of the square" and below which he adds:

Whether or not he saw these connections with transformational geometry, he was clearly fascinated in studying various stages in the process of a square image becoming round. On CA135va (fig. 798, 1492), for instance, he records a further stage in which the four circles nearly overlap one another completely. Accompanying this he drafts another passage which again emerges in more polished form on H227 inf. 49r (fig. 799):

CA135va H227 inf. 49r

It is a necessary thing that the It is a necessary thing that the

intersections of...round intersection of the round pyramid

pyramids is made in a single is made in a single closed point

point which is closed...of a of a non-transparent circumference.

non-transparent circumference. Therefore the half-round pyramid

It is necessary that the inter- will divide the point only

section made by the half-round surrounded by the half part, which

pyramid is amde in a point point you will find in the right

closed only...by the half part. angle and if you approach it to

the angle of the eye it will

appear to you in the form of a

half-circle.

On H227 inf. 50v (fig. 800) he considers a case where the distance is greater still and the image becomes completely round, losing all trace of the square aperture:

Of luminous bodies.

An understanding of this phenomenon how the image of a round light source passing through a square aperture is square at a close distance and round at a greater distance helps us, in turn, make sense of a passage on A64v (1492) that is puzzling if read out of context:

(Every aperture carries its form to the object over a long distance.)

Having considered the characteristics of triangular and square apertures, he explores slit-shaped apertures. On CA135va (1492), for example, he draws (fig. 802) a case where each of the two end-points of the slit produces a circle. He then redraws the slit (fig. 803) showing how the two circles overlap more at a greater distance. These diagrams are without text. When he pursues the problem on H227 inf. 51r-51v (fig. 801) he adds an explanation:

On CA135va (fig. 804, 1492) he also sketches a related case where two rectangular faces are positioned such that they produce an open slit. This he again draws and describes on H277 inf. 51r-51v (fig. 805):

On A64r 91492) he sketches (fig. 806) and comments briefly on another variant in which one slit is placed above another: "It is impossible that the luminous rays which have passed through parallels demonstrate to the object the form of their cause." On CA135va (1492) he sketches yet another variant in which the two slits are side by side (fig. 807). This he develops on H227 inf. 49v (fig. 808), explaining:

Having placed the two slits above one another and beside one another Leonardo explores the next logical combination in which the two slits intersect one another to form a cross-shaped aperture. On C9r (1490-1491) he illustrates (fig. 809) and describes a case where light source, aperture and projection plane are near one another, with the result that the image resembles the aperture:

On CA135va (1492) he sketches how each of the ends of the cross shaped image acquires a rounded shape (fig. 810). Next he shows how, at a greater distance, four circles emerge (fig. 811) which, at a greater distance still overlap more (fig. 812). Accompanying this he indicates the distances involved in quantitative terms:

The transit of solar rays through an angular aperture is necessary in some space.

On H227 inf. 49v 49v-50r, he illustrates (fig. 813) a situation where the distance is more than 30 braccia and the four circles are nearly coincident with one another. This he discusses in detail beginning with a general statement:

A specific description of the diagram (fig. 813) follows:

At a still greater distance the image loses all trace of the cross-shaped aperture and becomes

perfectly round like the light source. This situation he demonstrates (fig. 814) on C10v (1490-1491) beneath which he adds:

Leonardo has analysed in detail the properties of images passing through apertures in the form of triangles, squares, slits, double-slits and crosses. But he is not content to stop here. On C7v (1490-1491) he alludes to a more complex situation:

Perspective

Accompanying this he sketches in rough form an eight sided star (fig. 819). The problem is not forgotten. Within two years he describes this eight-sided star at length in connection with eight apertures on CA187ra (c.1492):

Remember that you note the quality and quantity of the shadows.

This entire description is written in the margin surrounding a carefully drawn diagram beneath which he writes:

In the lower right-hand part of this folio he has drawn (fig. 837) a draft of this octagonal star shaped aperture. Directly above this are four intersecting circles such as would result from a square aperture (fig. 815, cf. figs. 794-797). Beneath the principal diagram showing the shadows produced by the octagonal star (fig. 838) are three other diagrams of intersecting circles: two circles, as would result from a slit (fig. 816, cf. fig. 803), three intersecting circles, as would result from a triangular aperture (fig. 817, cf. figs. 784-785), and four intersecting circles as would result from a cross-shaped aperture (fig. 818, cf. figs. 811-812). In short, this octagonally shaped aperture marks the culmination of a series of experiments.

On CA256rc (c.1492) he drafts a summary of these results: "In the percussion of rays is demonstrated part of the nature of its cause." Which idea he then reformulates in a passage headed:

On the nature of apertures

10. Number of Apertures

If we return to read more carefully the passage on CA187ra (c. 1492), we find that he not only mentions an eight-sided aperture, but also eight apertures equidistantly arranged in a circle. This is not an oversight on his part. For just as he has been studying the properties of multi-sided apertures, so too has he been exploring the comparable properties of multiple pinhole apertures. On CA277va (1508-1510), for instance, where he outlines his new plan for arranging the work on light and shade (cf. Chart 10 above), he illustrates the image cast by one pinhole aperture (fig. 822), two (fig. 824), three (fig. 829), four pinhole apertures (fig. 834), and a rough sketch with the image cast by perhaps as many as eight pinhole apertures (fig. 838, although this could well represent an advanced stage in the rounding produced by three apertures, fig. 830, cf. 831).

These draft sketches on CA277va (figs. 822, 824, 829, 1508-1510) are developed on CA241rd (figs. 823, 825, 836, 1508-1510), this time accompanied by text. In the upper right-hand margin he notes in passing: "Many minimal lights in the long distance will continue and make themselves noticeable." In the main body of the text he drafts general rules of light and shade (see below, p. ). Alongside the drawings he discusses the:

Nature of the light which penetrates apertures.

Having answered his first two questions he considers the proportions of light involved under the heading:

Of the proportion that the impressions of light have placed partly one above the other.

To demonstrate this he now describes his figures (figs. 823, 825, 835, 836):

Further examples of four apertures occur on CA177rb (fig. 833); CA177vc (fig. 840, 1508-1510) he makes a rough sketch involving perhaps as many as eight apertures. On CA187ra (cf. fig. 838, 1492) he explicitly describes the use of eight apertures and on CA385vc (fig. 841, 1510-1515) he carefully draws apertures and the eight circles thereby produced. On the same folio he sketches two other cases with 18 apertures (figs. 842-843). This theme of multiple apertures is developed on CA241vc (1508-1510). Here he draws three intersecting circles which frame 24 apertures (figs. 845). Beneath this he draws another diagram (fig. 846) with 24 apertures to show how these, at a greater distance, produce 24 interlacing circles.

Accompanying these diagrams on CA241vc is a text that develops the ideas of CA241rc:

D

On light

This leads to a second general rule:

Of multiplied brightness taken from a single luminous body.

And this is proved in the 3rd, behind this face, etc.

On CA229vb (1505-1508) he takes this theme further. He begins with a rough sketch showing two circles inscribed within a larger one (fig. 847): this might represent a situation involving two apertures. He then draws (fig. 848) four apertures and the four circles thereby produced. There follow other examples which are multiples of four, beginning with a sketch (fig. 849) of 16 (4 x 4) apertures with a hint of the circles they produce. Next he draws (fig. 850) 12 points on a half-circle which would amount to 24 (4 x 6) apertures in all. A case (fig. 851) involving 21 (4 x 7) apertures follows. Finally he draws (fig. 852) a series of eight circles which span but a quarter of the circumference of a circle that would contain 32 (4 x 8) apertures. Of these various examples only the case involving 28 apertures (fig. 851) is accompanied with a text:

We have already noted Leonardo's implicit comparison between multiple sided apertures (triangles, squares, crosses, octagons) and multiple-apertures (1, 2, 3, 4, 8, 16, 24, 32 pinholes). On looking more closely at CA229rb, vb as a whole another, theme of comparison becomes apparent: he is analysing multiple-apertures on the same folio that he is exploring multiple shadows produced by a St. Andrew's cross. This is not a coincidence. His analyses of the multiple shadows produced by a St. Andrew's cross occur on CA37ra, 177rb, 177ve, 241rcd, and CA229rb, vb (see above pp. ). These are the very folios on which he also explores multiple aperture problems of light (see Chart 18).

CODEX MULTIPLE APERTURES MULTIPLE-SIDED MULTIPLE

APERTURES SHADOWS

CA177rb 4 4

CA177ve 4 6

CA241rcd 1,2,3,4 2,4

CA241vc 24 1 (on multiple

surfaces)

CA229rb,vb 4,16,24,32 2,4,6

CA277va 1,2,3,4, 3 1

CA37ra 1 (in various degrees) 2,4,6

CA385vc 8, 18 1,2,3,

CA187ra 8 2,3,4,8 2,3,4,8

11. Apertures and Interposed Bodies

We have examined how Leonardo explores the properties of light when it passes through apertures of various shapes such as slits and crosses. A next stage in complexity would be to study such apertures in combination with various shaped opaque bodies. This he does on CA187va (c. 1492) where he makes a series of preliminary sketches to show what happens when light passing through a slight-shaped opening encounters a spherical object (figs. 853-854, 856-862). Above these diagrams he makes two drafts of an explanation:

Unsatisfied, he crosses out these drafts. He turns the sheet ninety degrees and makes two further sketches showing how light, having passed through a slit, and encountering a spherical object, produces a combination of simple and mixed shadow (figs. 855, 864). In the left-hand margin he drafts a phrase: "That light which," then stops short. Alongside the lower diagram he notes: "This light is long and then." Directly beneath this he writes: “No separate shade can stamp on the wall the true form of the umbrous body, if the centre of the light is not equidistant from the extremities of this body.” In the upper left-hand margin he now claims: “No long light will send the true form of the separate shadows (to the wall) from the spherical bodies to the wall.” On CA187ra (1492) he redraws his sketch of light passing through a slit, which encounters a sphere and casts shadows on the wall (fig. 863). Alongside this figure he writes: "Remind yourself that you note the qualities and the quantities of the shadows." On A89v (BN 2038 9v, 1492) he redraws the situation (fig. 865) and on A89r (BN 2038 9r, 1492) he develops it into a beautiful diagram without text (fig. 866). As is so often the case, he expects that his visual statement will speak for itself.

Closer attention to the other sketches on CA187ra (1492) again reveals Leonardo's delight in playing with variables. Having shown what happens when a slit-shaped light encounters a spherical opaque body (fig. 863), he considers what occurs when a spherical light encounters a slit-shaped opaque body (fig. 867). Not content to stop here he lets light pass first through a round and then through a slit-shaped aperture (figs. 868-869) and contrasts this with light which passes first through a slit-shape and then through a round aperture (fig. 870). Next he replaces this slit-shape with a cross shape (figs. 871-875).

This final example can be seen as a starting point for his illustration more than fifteen years later on CA207ra (fig. 876, c. 1508-1510) to "make a crucifix enter a room." Here he takes a blank wall on which he marks a crucifix. Opposite this wall he positions an aperture which is in a room. The sunlight reflects the light of the wall, enters through the camera obscura and casts the image of a cross into the room, (cf. Kircher's later example, fig. 877).

A more complex play with cross-shaped images is suggested on Triv. 22v (fig. 878, 1487-1490) which may be the basis of his diagram on C11r (fig. 879, 1490-1491) where light passes through a cross-shaped aperture, encounters a transparent sphere and then casts a rounded cross-shaped shadow. Accompanying this he notes:

The shape of the derived shade will always have conformity with the form of the original

shade.

In 1508, he returns to this problem of cross-shaped images, now in an unexpected context. On F28v (fig. 880) he observes that:

By way of illustration he makes two sketches to show how smaller bubbles13 surrounding the larger bubble (figs. 881-882) might serve to generate a cross-shape. On CA236rd (1508-1510) he makes a note: “on the shadows situated at the bottom of the water and which send their species to the eye through water and through the air,” but proceeds to discuss refraction (see below p. ). He appears not to have pursued the problem of cross-shaped bubbles as he had hoped.

In the period 1508-1510 he does return, however, to problems of slit-shaped apertures and opaque bodies on CA258va. Here he begins (fig. 883) with light passing through a slit-shaped aperture which encounters a narrow opaque body and casts a shadow on the ground at ninety degrees to this. Directly beneath he explains:

Next he considers a situation where this shadow is cast at more than ninety degrees (fig. 884):

Immediately following he turns to the converse:

There follows the converse of the said.

To illustrate this he moves an interposed stick through various degrees of obliquity (fig. 885). Finally he considers a case where a slit-shaped aperture, thin opaque body and the resulting shadow are all in the same plane (figs. 886-887)

This situation interests him and on CU630 (TPL627, 1508-1510) he examines it in more detail under the heading:

Of the derived shade created by light of a long shape which percusses an object similar to it.

A specific demonstration follows (fig. 888):

Having studied in isolation the effects of different shapes of umbrous bodies and apertures, he examines various situations where these factors act in combination. On C9v (1490-1491), for instance, he draws a light source (fig. 889) the rays of which, on meeting an opaque body, cast a shadow which passes through an aperture. On the far side of this aperture are two further light sources g and h which cast rays intersecting this shadow. Directly beneath this diagram he adds a brief text:

On W12352v (c. 1494) he draws another diagram (fig. 890) of a luminous body the rays of which meet an opaque body and cause shadows which then pass through an aperture. Here there is no accompanying text. But then on CA236rc (1508-1510) he redraws the diagram carefully (fig. 891) and adds a full explanation under the heading:

What difference there is between shadow and image.

Meanwhile, on CA216rb (c. 1495) he had been exploring more complex variants of this situation. In a first diagram (fig. 892) a light source is left undrawn and an opaque object casts its shadow through two apertures onto a wall. In a second diagram (fig. 893) there are again two apertures, but now there is an opaque body in front of these apertures and a smaller opaque body behind them. Their shadows combine to produce a series of four intersecting circles. Finally there is a third diagram (fig. 894) which has the same elements and differs only in that relative sizes of the opaque bodies are changed. There is no text accompanying these diagrams.

On CA238vb (1505-1508) he takes a flat rectangular board and a round ball. These he places in near proximity to one another in order that they effectively function as an aperture. He then examines the effects produced by moving the light source and altering relative positions of the board and ball. Accompanying the series of diagrams that result (figs. 895-963) he drafts a number of only half intelligible notes which are here translated without comment:

All [fig. 901] the luminous rays that are cut by n are lacking at m.

(The umbrous body outside the window)

(The solar rays)

(Here the shadow of the board carried by solar rays).

Of which it happens (that the)

(Here) many correlates, that is derivatives.

(Here the...solar rays which terminate the shade)

Of the circle.

The umbrous body inside the window, the sun always....

ae /fig. 897/ is the lower limit of the shadow of the board.

Related diagrams are to be found on CA238rb (figs. 712-719, 1505-1508) and CA133va (figs. 904-909, 1497-1500. With two exceptions these are without text. Beneath one (fig. 908), he points out that "the line ab is the boundary of the luminous body." Below the largest diagram (fig. 909) he writes: "When n touches m, f will touch g." On such folios which represent an interim stage int eh development of his ideas, rough sketches suffice. Careful explanation is not yet necessary.

12. Spectrum of Boundaries

Leonardo's studies of a camera obscura in combination with opaque bodies lead him to abandon his early assumptions concerning clearly defined boundaries and to emphasize instead a spectrum of gradations between light and shade. This he does in terms of demonstrations involving a series of basic arguments: (1) that derived shade has less power to the extent that it is more distant from its primitive shade; (2) conversely, that derived shade has more power when it is closer to its source; (3) to what extent one can speak of uniformity of derived shade; (4) that primitive and derived shade mix with distance; (5) where primitive and derived shade are joined together; (6) where shade is greater; (7) where primitive and derived shade are not joined; (8) implications for the perception of backgrounds and (9) simplified gradations of shade.

We shall consider his demonstrations for each of these arguments in turn and show how these interests lead directly from the physics of light and shade to problems of vision and perception.

12.1 Derived Shade is Less Powerful When More Distant From Its Primitive Shade

The idea that derived shade loses strength with distance is clearly expressed on CA258va (1508-1510):

He mentions this idea in passing on CU705 (TPL553d, 1508-1510): "The darkness of the derived shade diminishes to the extent that it is more remote from the primitive shade." On CU707 (TPL561, 1508-1510) Leonardo returns to this problem in greater detail in a pass age entitled:

On compound derived shade.

A concrete demonstration (fig. 924) is cited in support:

12:2 Derived Shade is More Powerful When Closer to Primitive Shade

On CA144va (c. 1492) he drafts this idea: “The closer that the derived shade is to the primitive to that extent is it darker...and its boundaries are less /than the/...luminous part that surrounds it.” This he crosses out. On CU730 (TPL598, 1508-1510) he takes up this claim afresh under the heading:

Whether the derived shade is darker in one place than in another.

He reformulates the idea on CU699 (TPL606, 1508-1510) under the heading:

Of the boundaries of derived shade.

Immediately following the objects of an adversary are mentioned and answered:

12.3 Uniformity of Darkness

The above two demonstrations serve as basis for his comments on CA258va (1508-1510):

On the Uniformity of Derived Shade.

12.4 Primitive and Derived Shade Mix With Distance

The concept that primitive and derived shade mix with distance is implicit in a statement on CA256rc (c. 1492): “To the extent that the umbrous body is closer to the percussion of the rays its shadow will observe the form of its derivation more.” On CA144va (c. 1492) he drafts an idea: “(That part of the derived shade will mix itself less with its boundaries in the light that surrounds it which is closer to the primitive shade.)” This he crosses out and makes two further drafts:

One reason for this claim stems from everyday experience as is clear from a passage on A92v (BN2038, 2v, 1492): “How the shadows are confused over a long distance is proved in the shadows of the moon which are never seen.” On CU636 (TPL438a, 1505-1510) he returns to the general problem in passing: "and the derived shade mixes itself the more with the light to the extent that it is more distant from the umbrous body." Which idea he reformulates on CU699 (TPL606, 1508-1510): "That shade is more distinct and defined which is closer to its origin, and the more distant is the least defined," and on CA371rb (1510-1515) he expresses it differently again:

12:5 How Primitive and Derived Shade are Joined Together

Related to the foregoing is a demonstration on CU697 (TPL562, 1508-1510) entitled:

How primitive and derived shade are joined together.

By way of illustration he gives a concrete example (fig. 925):

This theme he pursues on CU708 (TPL563, 1508-1510) headed:

How simple shade is conjoined with compound shade.

A demonstration without an illustration follows:

And leads to a second claim:

Which, in turn, is demonstrated, again without an illustration:

12.6 Where the Shade is Greater

On Forst III 87v (c. 1493) Leonardo mentions how the extremities of shade are affected by light:

The luminous or illuminated object bordering on the shade intersects as much as it cuts.

On H66/18/(r) (January 1494) he notes: "that part of the derived shade will be less dark which is more distant from its extremities." He returns to this idea in two drafts on CA190rb (1505-1508):

On this same folio he also drafts another phrase: "That object will make itself darker which is...seen by a greater amount of darkness." The way in which this and related themes are associated in Leonardo's mind is seen clearly on CA230rb (1505-1508) which opens with a series of general claims and a questions:

The boundaries of the maximal derived shade is darker than its middle.

The surface of every opaque body participates in the colour of its object.

Why shades tinge dense bodies and not rare ones?

This is followed by a further question:

This is answered with the help of a demonstration (fig. 911):

The accompanying diagram (fig. 911, cf. figs. 910, 912) recalls his studies of divergent shade (see above pp. ). Above this diagram he adds a brief caption: "To the extent that g /and/ i are less, to that extent are the whites surrounding maximal shade narrower." To the left of this he draws a further diagram (fig. 913, cf. figs. 912, 914-915), beneath which he explains:

Which explanation continues in the next column to the left:

He restate this conclusion in passing on CU699 (TP606, 1508-1510); "The shade will show itself as darker towards the extremities than towards its centre," and sets out to demonstrate it afresh on CA195va (fig. 930, c. 1510):

And in their boundaries colours are more intensive and brighter than their parts.

Later on the same folio he pursues this theme asking (fig. 930):

First reply.

Such investigations lead him to examine precisely where gradations of light and shade are brighter or darker. On CA297va (1497-1500), for instance, he makes a preliminary sketch (fig. 916) which he then redraws (fig. 917) and describes:

And the 3rd line pq sees the entire umbrous body cp and all the luminous body ac.

Roughly a decade later he takes up this theme afresh on CA37ra (1508-1510). He now draws two preliminary diagrams (figs. 918-919) and then a third (fig. 920, cf. figs. 921-922). As usual, the accompanying text opens with a general statement:

A demonstration follows (fig. 920):

He now writes a new heading: "Of the middle contained by the extremities." He is, however, unsatisfied and crosses out the entire passage. In the right-hand margin he begins afresh:

This divides itself into 4: 1st: of the extremities containing the compound shade.

2nd: of the compound shade within the extremities.

Again he breaks off and in the lower centre of the folio he notes in passing: "Where the shade is greater or less or equal to the umbrous body, its origin." He now turns the folio to the side, draws a considerably more complex diagram (fig. 923) and analyses it in a passage headed:

Of the shade bch.

He pursues this theme of various gradations of brightness and darkness on CA258va (1508-1510) beginning with two demonstrations (figs. 956):

An interim paragraph follows in which he introduces the question of maximum brightness.

To this end a further demonstration follows:

He returns to this theme on CU669 (TPL719, 1508-1510) under the heading:

Of the brightness of derived light

The diagram for the demonstration that follows is reminiscent of earlier discussion in this context (fig. 926, figs. 924-925):

And through such a discourse we have proved that r is the brightest part of the pavement qs.

12.7 Where Primitive and Derived Shade are not Joined

On CA258va (1508-1510), having discussed conditions under which primitive and derived shadow are joined he considers (fig. 928):

Of the shadow that does not join the derived and the primitive.

A similar diagram and demonstration are found on CA195va (fig. 929, 1508-1510) where he observes:

These diagrams are the more interesting because they return to a problem that had perplexed him in his earlier studies of light and shade, namely, what causes the shadow of an opaque body smaller than the light source to be divergent.

On CA195va (1510) he draws (fig. 930, cf. 931) a camera obscura in which the entering light encounters two opaque bodies and produces complex gradations of light and shade, which he describes briefly: “op sees and is seen by ab and is tinged by its colour and on the side p is seen the beginning of the brightness of the air which brightens the place where its image percusses.” Hence this combination of camera obscura and opaque objects provides yet another demonstration for his "colour participates" argument (see above pp. ).

12.8 Implications for The Perception of Backgrounds

At the same time this demonstration serves as a starting point for a further argument.

This particular demonstration is of considerable interest because, as will be shown (see below pp.** ) he had made various experiments to establish the contrary, namely, that, white on a black background appears whiter and black on a white background appears darker. On this same folio he explicitly compares the effects of a camera obscura with those of the pupil in the eye. Problems relating to physics of light and shade, the physiology of vision and perception are all intimately connected in Leonardo's mind. As a result what had traditionally been philosophical and psychological questions of vision and perception now emerge as problems of physics. Problems of optics are no longer a matter of theoretical debate but open to practical verification by experiment. He returns to this situation of a sphere placed within a camera obscura once more on W19086r (K/P178r, fig. 927, c. 1513) where he notes that:

12.9 Simplified Gradations of Shade

Parallel with these demonstrations is a further series which omits the interposed opaque sphere and reduces the problem of gradations of shade within the camera obscura to its essentials. Preliminary drawings (figs. 932-941) on this theme are found on CA345rb (1505-1508) amidst discussions of species being everywhere in the air (cf. pp.** ) and how things cannot be seen without apertures (cf. pp.** ). Among these ten drawings, only one is explained (fig. 941):

On CA190rb (1505-1508) this theme of gradations of light/shade within a camera obscura is developed. In the right-hand column he begins with a preliminary sketch (fig. 942), beneath which he draws a camera obscura with various gradations (fig. 943). To this diagram he adds six letters. These, however, are not explained. Beneath the diagram he merely notes: "That object will be darker which is seen by a greater sum of darkness." He now draws two further diagrams showing gradations of shade in a camera obscura (figs. 944, 947) and in the passage that follows describes the one on the right under the heading:

A precise description of the figure now follows:

Here the right-hand column ends. In the upper left-hand column he drafts two further diagrams (figs. 945-946) beneath which he drafts an explanation of the left-hand figure:

h sees the weak limit of the light and sees...the maximum darkness of the maximum shade such that in this h one sees entirely shade.

Here his manner of referring to different fractions of light and shade strikes us as familiar. We have encountered it on more than one occasion (see above pp. ). His references to maximal light and shade we have also encountered elsewhere (CA258va, CA230rb, CA345rb). But if the initial thoughts remain similar, their applications are, nonetheless, quite different.

This diagram in the upper left-hand margin is probably a draft for the left-hand diagram (fig. 947) in the right-hand column, which he describes after he has crossed out his draft:

Here the text breaks off and he gives instructions to turn the "page" to CA190vb (1505-1508) which opens:

O mathematicians throw light on such error.

This is reminiscent of a passage on CA345 (see above pp. ) which also occurs in connection with a camera obscura passage. The lower part of CA190vb contains various diagrams relating to the inversion of images within the eye (figs. ) to be discussed later in section three. Amidst these diagrams he draws another preliminary sketch of a camera obscura with its gradations of shade (fig. 948), beneath which he draws two more elaborate versions (figs. 949-950), the latter of which appears intended to serve as an imitation eye. Alongside this figure he adds a text which is interrupted:

Here the transition from physics of light and shade in a camera obscura to problems of vision and perception remains implicit.

13. Camera Obscuras and the Eye

On D10v (1508) this analogy is taken one step further. Here towards the centre of the right-hand column he draws a camera obscura with various gradations of shade (fig. 951). Above this he writes: "first." Above this, in turn he draws an eye in which various rays are being inverted at the pupil (fig. 952). This figure is headed: "second." Between these two figures he adds a brief marginal note:

Lower down the same right-hand column this perceptual problem is pursued:

Here the bridge between Leonardo's physics of light and shade and his physiology of vision is manifest. Indeed it is clear how his camera obscura studies which make him aware of differing gradations of light and shade influence both his theories of perception and painting. Leonardo returns to these themes briefly on CA195va (c. 1510) which, as has been noted, is another of those folios on which the camera obscura-eye analogy is explicit (see above pp. ). In the lower left-hand portion of this sheet is a rough sketch (fig. 953) of a camera obscura with five gradations. In the lower centre is a slightly more developed version (fig. 954) with seven gradations and near the bottom is an example with nine gradations (fig. 955). Each of these three possibilities is duly recorded in a brief note: "Make five or 9...or 7 spaces in ir in order that the white no stands in the middle." Beneath this is a further passage which partly explains the bottom diagram (fig. 955):

Even if this text is interrupted, the accompanying diagrams remain of considerable interest because they reveal that Leonardo is trying to quantify gradations of shade. He wants, as far as possible, to measure what had previously been a purely subjective problem and thereby he brings the field of optics one step closer to its modern position as a branch of mathematical physics.

14. Conclusions

Although it is generally known that Leonardo worked with the camera obscura and compared the inversion of images in this instrument with those of the eye, scholars often refer to these facts as if they were only mentioned in passing in the notebooks. Our comprehensive study of the topic has shown that Leonardo devoted no less than 270 diagrams to the theme of camera obscuras and that these interests grow in part out of the astronomical tradition.

He uses the camera obscura to demonstrate not only the inversion of images but also that images passing through an aperture do not interfere with one another, that images are all in all and all in every part, that pinhole apertures produce different intensities of light and shade and that inverted images demonstrate a contrary motion.

Mediaeval optical writers had given considerable attention to the images of round light sources passing through triangular and other complex apertures. Leonardo studies the problem systematically in the case of triangular, square, octangular, slit-shaped and cross-shaped apertures. He demonstrates that whether the shape of the projection resembles the aperture or light source depends on the relative distance of these factors. He does not attempt to arrive at a formula for these relationships but he does give some quantitative references to his experiments.

In addition he studies situations with 1, 2, 3, 4, 8, 16, 24 and 32 pinhole apertures. He also studies the effects of light which passes through apertures of different sizes and encounters various interposed objects. Such experiences lead him to new studies of gradations of shade which prompt further analogies with problems of visual perception: why, for instance, the eye cannot perceive clearly the boundaries of nearby objects.

The great importance of these extensive studies of the camera obscura is that they bring various questions concerning the nature of light and shade and vision into the experimental domain of physics. Optics is no longer a problem for philosophical discussion: it is now a domain which requires scientific demonstration. In the section that follows we shall see how this mentality also leads Leonardo to make physical models of the eye. If the answers he finds are not always correct, the new kinds of answers he seeks are nonetheless important.

Part Two Chapter Three The Camera Obscura

1. Introduction 2. Astronomical Context 3. Inversion of Images 4. Non-interference 5. Images all in all 6. Intensity of Light and Shade or Image 7. Contrary Motion 8. Size of Aperture 9. Shape of Aperture 10. Number of Apertures 11. Apertures and Interposed Bodies 12. Spectrum of Boundaries 13. Camera Obscuras and the Eye 14.Conclusions

Introduction

Leonardo has commonly been credited with the invention of the camera obscura⁹. This is not true. Unequivocal descriptions of the instrument go back at least until the ninth century A.D.¹⁰ and by the thirteenth century it had assumed an important function in astronomy.¹¹ On the fourth of June, 1285, for instance, William of St. Cloud used a camera obscura to observe an eclipse of the sun.¹² This use of the camera obscura develops in the fourteenth century and in the latter fifteenth century provides one source of Leonardo's interest in the instrument. He uses it, for example, to estimate the size and distance of the sun and moon.

The aperture of the camera obscura is, for Leonardo, analogous to the aperture of the pupil and this leads him to study various characteristics of apertures: how images passing through them are inverted, how they do not interfere with one another, how such images are "all in all and all in every part"; how they can vary their intensity, and how they move in a contrary direction beyond the aperture.

He considers the effect of changing the size of the aperture and examines in some detail both the properties of a single aperture with a changing number of sides and the characteristics of multiple pinhole images. From a note on CA277va (1513-1514) cited above (see p. ), he clearly intended to adopt these findings for two additional books on light and shade. Indeed many of the experiments that he had made with umbrous bodies in the open he repeats in combination with a camera obscura, now focussing on a particular phenomenon: how the boundaries between light and shade are actually a series of subtle graduations. These late studies of 1508-1510, as will be shown, have important consequences for his theories of vision and perception. But before considering these, we need to examine the details of his camera obscura studies.

Astronomical Context

Leonardo's earliest extant reference to the use of an aperture in observing eclipses is on Triv.6v (fig. 678, 1487-1490):

In this case the image is seen directly and the aperture serves merely to screen off excessive light. On CA270vb (c. 1490) he describes a case where the image is seen indirectly under the heading:

How bodies...send...their form and heat and power beyond themselves.

When the sun, through eclipses, remains in the form of the moon, take a thin sheet of iron

and in this make a little hole and turn the face of this sheet towards the sun...holding a piece

of cardboard a 1/2 braccia behind this and you will see the similitudes of the sun come in a

lunar shape, similar to its shape and colour.

Immediately following he offers a (cf. fig. 679).

Second example.

Finally he provides an illustration that simulates the effects produced by these natural phenomena:

Third example.

This example, described on CA270vb, is illustrated in diagrams on CA126ra (fig. 156), CA125vb (fig. 694), and CU789 (fig. 704). The case of the moon is also considered on A64v (1492):

Because all the effects of luminous bodies are demonstrative of their causes, the moon in

the form of a boat, having passed through the aperture, will produce at the object /i.e. the

wall/ a boat shape.

On A61v (1492) he pursues this theme, now adding an illustration (fig. ):

That perforation of round quality which is half closed will appear in the form of ab and the

part c will be the light and n will be the closed off part and this same happens to the

luminous half-moon.

The problem of the moon's shape continues to perplex him. On CA243ra (1510-1515) he notes:

Since over a long distance a long luminous source makes itself round to us and /yet/ the

horns of the moon do not observe this rule and even the light from nearby observes the

demonstration of its point.

The use of the camera obscura in determining the diameter of the sun had been discussed by late mediaeval authors such as Levi ben Gerson5 (c.1370). This also interests Leonardo as is shown by a diagram on A20v (fig. 679, cf. A21r, fig. 680 and Mario BEttini, fig. 681) beneath which he adds:

Way of knowing how large the sun is. Make that from a /to/ b there are hundred braccia

and make that the aperture where the solar rays pass is 1/16 of a braccia and note how much

the ray has expanded in percussion.

The problem is not forgotten. On CA225rb (1497-1500) he reminds himself in passing of "the measurement of the sun promised me by Master Giovanni the Frenchman." On BM174v (1500-1505) Leonardo describes a more complex procedure involving a combination of camera obscura and mirror (fig. 682):

ab is the aperture through which the sun passes. And if you could measure the size of the

solar rays at nm, you could see very well the true lines of the concourse of these solar rays,

the mirror standing in ab, and then make the rays reflected at equal angles towards nm. But

The precise function of this procedure is not explained. On Leicester 1r (1506-1509) he alludes to but again does not elaborate on a

To this problem of sizes and distances of the planets he returns on CA243rb (1510-1515) now providing a more detailed explanation:

If you have the distance of a body you will have the size of the visual pyramid which you will cut near the eye on the window (pariete) and then you remove the eye to that extent, such that the intersection is doubled, and note the space from the first to the 2nd intersection and say: if in so much...space the diameter of the moon increases so much above the first intersection, what will it do in all the space that there is from the eye to the moon? This will make the true diameter of this moon.

The method here described is identical to the surveying procedure used to demonstrate principles of linear perspective on CA42rc, (cf. vol. 1, fig. 122). On CA151va (1500-1506) he gives an alternative method of measuring the distance of the sun, this time using a staff again familiar from the surveying tradition. Lower down on CA243rb he draws a rough sketch of a camera obscura (fig. 683) beneath which he notes "Measure of the size of the sun, knowing the distance." On CA297va (1497-1500) he drafts a passage concerning the use of apertures in a meteorological context:

This he drafts again directly below:

These drafts serve in turn as the basis for a passage on CU476 (fig. 684, TPL447, 1510-1515):

On the solar rays that penetrate the apertures of clouds.

Also in this late period, on CA248va (fig. 685, 1510-1515), he again mentions the relative intensity of the sun's illuminating in a camera obscura:

These astronomical and meteorological uses of the camera obscura constitute but a small part of Leonardo's concern for this instrument. He is fascinated by the analogies that it offers with the pupil (see below pp. ) and therefore employs the camera obscura to demonstrate such optical principles as inversion of images, their non-interference, and their existence "all in all and all in every part." We shall examine each of these in turn.

Inversion of Images

Leonardo believes that images are inverted in passing through the aperture of the pupil. As early as 1489-1490 he employs a camera obscura to demonstrate this principle in a passage on W19147v (K/P 22v):

A specific example follows (fig. 686):

He pursues this eye-camera obscura analogy on C6r (fig. 688, 1490-1491):

He illustrates this inversion principle in sketches without text on Forst III 29v (fig. 869, 1490-1493), CA155rde (fig. 692, 1495-1497) and BM170v (fig. 692, 1492); then mentions it again on BM232v (1490-1495): “The bases of inverted pyramids, if they are in a dark place, will show upside down the shape and cause of their source.” A further illustration occurs on CA125vb (fig. 694, 1492) accompanying which he drafts an explanation:

On CA126ra (c. 1492) the problem is further illustrated (fig. 156). Thereafter, more than a decade passes before he broaches the problem again on CA345vb (figs. 695-696, 1505-1508):

In the Manuscript D he discusses the problem of inversion at length. A first passage on D10r (c. 1508) is entitle:

Of the species of objects that pass through narrow apertures into a dark place.

To demonstrate this he provides a concrete example (fig. 697):

On D8r he pursues this analogy between eye and camera obscura under the heading:

How the species of objects received by the eye intersect inside the albugineous humour.

A concrete demonstration follows (fig. 698):

He again mentions this way in which images are inverted in passing on W19150v (K/P 118v(a), fig. 699, 1508-1510): "No image of however small a body penetrates the eye without being turned upside down....." On CA241vc (also 1508-1510) he produces two further drafts:

These he crosses out and reformulates:

4. NON-INTERFERENCE

The non-interference of images is another phenomenon which he demonstrates using the camera obscura. On A93r (BN2038 13r, 1492), for instance, he shows how a red, white and yellow light can intersect without interference (fig. 700). Similar demonstrations occur on CA256rc (figs. 701-702, c.1492) involving a red, green and yellow light and a red, white and green light. Accompanying these are a series of draft notes concerning the intensity of colour, light and shade passing through apertures:

The qualities of rays are 2, that is: luminous and umbrous.

On 19112r (K/P 118r, 1508-1510) he returns to the theme of non-interference of colours in a camera obscura, this time using yellow and blue lights (fig. 703). Slightly more complex is a demonstration on CU789 (fig. 704, TPL707, 1508-1510) where he shows how light from a candle and from the air produces different colours on an interposed object:

Of the colours of lights illuminating umbrous bodies.

On CU797 (TPL645, 1508-1510) he had used a similar demonstration to establish that the colour of shadows participates with the colour of surrounding objects (see above pp. ). On W19150v (fig. 705, K/P 118v, 1508-1510) he pursues both the themes of colour participating and non-interference of images under the heading:

Of the rays which carry the images of bodies through the air.

And let r be one of the sides of the opening. Opposite this, let s be an eye which sees the lower extremity u of the line no, which extremity cannot send its similitude from itself to such an eye s such that it does not touch the extremity r and m, the middle of this line does the same and the same happens to the upper extremity n /going/ to the eye /at/ v. And if such an extremity is r, the eye v does not see the colour green of o at the edge of the aperture, but only the red of n by the 7th of this where it is stated that every similitude sends its species beyond itself by the shortest line which, by necessity, is straight etc.

On the recto of this same folio (K/P 118r) this phenomenon of the non-interference of images is discussed further in a passage entitled:

(figures)

This claim he qualifies:

5. IMAGES ALL IN ALL

The way in which Leonardo uses a camera obscura to establish that images are all in all and all in every part has been analysed previously (see above pp. ). This was chiefly in terms of passages on A9v (fig. 133, 1492) and W19150v (figs. 706-706, K/P 118v, 1508-1510). This principle is also implicit in a sketch on BM171r (fig. 708, 1492) beneath which he writes:

It is equally implicit in other sketches on W12352v (fig. 709, 1494), CA91vb (fig. 710, C.1500), CA112va (fig. 711, 1505-1508), as well as in a series of sketches (figs. 712-726) on CA238rb, vb (1505-1508) accompanying which is only an interrupted text: “Every part of ab...is in every part...d, but more...illuminate...short ray...where the spe/cies.../ powerful occupy...the less powerful.” On CA155rd (figs. 729-732, 1497-1500) he implicitly demonstrates this principles again in a series of four diagrams accompanying which he merely notes:

abfik is according the adversary; abcgh is mine.

This principle is illustrated roughly once more in a diagram without text on W12353 (fig. 734, 1508-1511).

6. INTENSITY OF LIGHT AND SHADE OR IMAGE

Images in the camera obscura may be "all in all and all in every part." Nonetheless, Leonardo is convinced that they can vary in their intensity, and he uses the camera obscura to demonstrate this. On C14v (1490-1491), for instance, he draws a rough diagram (fig. 735) which he then develops (fig. 736). Accompanying this he opens with a general comment:

This is followed by a specific demonstration, which refers back to the diagram (fig. 736):

This theme of differing intensities of light within the camera obscura is mentioned in passing on CA256rc (fig. 733, 1492): “The luminous rays make the shadows of bodies greater which are opposite the aperture and the percussion, which bodies are touched by a less luminous ray.” On CA238rb (1505-1508) following the all in all passage cited previously (see above p. ), he again takes up this theme of differing intensities of light and shade (fig. 723):

He now draws a second diagram (fig. 724) which he explains:

Therefore experience showing how the percussion of luminous rays acquires degrees of darkness in every part of height and this not being concluded by the first figure the second concludes it, because all the light ae sees i and 3/4 of this light be sees h and half the light ce sees g and a quarter of the light...de sees f. Hence f is less luminous and 3/4 so than i.

Another diagram follows (fig. 726 cf. 727-728) accompanying which he notes: "When the motion is from n to m, the shadow will descend from a to b." On this single folio CA238rb (1505-1508) he has thus used a camera obscura to demonstrate that (1) images are all in all and all in every part (see above pp. ); (2) that images vary in their intensity and (3) that images inside a camera obscura are inverted mind these three demonstrations are closely related. It is no wonder, then, that the remaining preparatory sketches on this folio (figs. 715-719, 722, 725) which are without text have a certain ambiguity about them: they could serve to support any of or all three of these demonstrations.

On C12v (fig. 737, 1490-1491), in the course of his studies of light and shade, he had illustrated how a light source in front of two opaque bodies produces concentric rings of light and shade of different intensity. The text on C12v is closely related to a draft, possibly in another hand on BM101r (1490-1495):

BM101r C12v

That umbrous body of spherical That umbrous body of spherical

rotundity will make circular rotundity will make circular mixed

mixed shade which will be be- shade which has placed between it

tween it /and/ the sun a body and the sun an umbrous body of its

placed opposite it similar to quality.

its quality /and/ quantity.

This demonstration of concentric rings caused by opaque bodies in the open air is the more interesting because it is paralleled by further demonstrations involving camera obscuras. On CA242v (1497-1500), for instance, he draws (fig. 738) sunlight entering through an aperture which is intersected at various distances. Directly beneath he describes the first percussion:

He then describes the second percussion

And the said space ab is seen by op and the space cd by nm which obscure it.

A description of the third percussion is given short schrift: "At the 3rd figure bc is seen by all the body of the sun."

He pursues this theme on CA262ra (1497-1500). Here he carefully redraws his diagram showing various percussions of sunlight within a camera obscura (fig. 739). Directly above this he drafts a general claim: “The solar ray which penetrates inside the apertures (of the eye) of houses, in each degree of its length changes quality as quantity.” It is noteworthy how he here writes "apertures of the eye" which he then crosses out to write "apertures of houses." The correction is significant because on the same folio he also discusses different kinds of pupils (see pp. ). The camera obscura-eye analogy is very important for him. Not content with his first draft he crosses it out and begins afresh:

Here the text breaks off. Beneath the diagram he starts anew, now with a description of the 6th percussion.

He returns to this theme in a sketch without text on CA238rb (fig. 740, 1505-15087). In the Manuscript F similar sketches becoming a starting point for theories of the pupil (figs. , see below pp. ).

7. CONTRARY MOTION

Leonardo's use of the camera obscura to demonstrate the phenomenon of contrary motion can be traced back to a note on C3r (fig. 741, 1490-1491):

He pursues this theme in a series of sketches without text on CA357rb (figs. 744-748, c. 1490). On CM171v (1492) the principle is again mentioned:

Further sketches (figs. 742-743) without text follow on CA133va (1497-1500). Approximately a decade later he demonstrates this principle of contrary movement of images in a camera obscura by moving the edges of the aperture on W19149r (K/P 118r, figs. 749-751, 1508-1510, see above pp. ). In this same passage he also broaches the themes of aperture size, rectilinear propagation and the principle that images are all in all in every part.

Gis. 752-756: Experiments concerning contrary motion of images in a camera obscura on CA277va.

The principle of contrary movement is further examined on CA277va (1508-1510). Here his approach is experimental and systematic. He begins with a situation (fig. 752-753) where a stick, situated in a high position in front of a near wall, casts a shadow low down on the far wall. The accompanying text is headed:

Operation of compound shade.

The operations of compound shade are always of contrary motion.

Having considered the contrary motion of this stick's shadow when the stick is positioned in front of the first wall (fig. 754), he explores what happens if the stick is positioned behind this first wall:

Next he turns to a case where the stick is positioned in the same plane as the first wall (fig. 755, cf. fig. 756):

This passage ends with a general comment:

He returns to this theme of contrary movement on E2v (1513-1514) in a passage headed:

On shadow and its movement.

This he demonstrates with a concrete example (fig. 757):

8. Size of Aperture

Concerned as he is with studying the variables of a given problem it is not surprising to find him exploring the role played by different sizes of aperture. On CA373rb (1490-1495) he merely makes two preliminary diagrams without text (figs. 758, 762). These he develops in two diagrams (figs. 759, 763) on CA256rc (1492) where he draws a thin and a thick wall alongside which he writes: “Among apertures of equal...size that which is in a larger wall will render a darker...and smaller percussion.” On H227 in f. 47v=48r he takes these ideas further. Here he draws a thick wall (fig. 760) accompanying which he notes: "The aperture that is positioned in a thick wall will give little light to the site where it reaches." He also draws a thin wall (fig. 764) with the comment: "That aperture that is positioned in a thinner wall will give more light to the place where it reaches." He pursues this theme on A2r (fig. 761, 1492) where he draws a relatively thin wall and considers changing intensities of light inside a camera obscura under the heading:

Quality of lights

On A85r (BN2038 5r, 1492) he draws a related diagram (fig. 765) alongside which he drafts an explanation:

Not content, he crosses this out and reformulates it under the heading of:

Painting

He redraws the diagrams of A2r and A85r on CA262v (figs. 766-768, 1497-1500) this time with no accompanying text. About a decade later he takes up this theme of apertures of different sizes once more in W19152v (K/P 118v, 1508-1510), beginning with a general claim: “Images which pass through apertures into a dark place intersect their sides that much nearer to the aperture to the extent that this aperture is of lesser width.” By way of illustration he draws three diagrams and first discusses the case (fig. 769) on the far left in which the opaque objects ab and ik produce shadows which pass through the aperture de:

Gis. 769-771: Demonstrations of concerning different sizes of aperture in camera obscuras on W19152v (K/P 118v).

He proceeds to discuss the two figures to the right of this, namely, abc, which is on the far right, (fig. 771) and nmo which is on the near right (fig. 770, or as he puts it, to the left relative to abc):

He then considers further properties of the diagram at the far left (fig. 769):

This discussion of where image formation occurs leads him to mention where images are doubled:

Here the physics of light and shade dovetails with the problem of image formation in a camera obscura which interests him because of its relevance to vision (see below pp. ). In Leonardo's mind one topic constantly leads to another.

These interweaving analogies he develops on CA385vc (1510-1515) where he sketches two examples with two opaque bodies (figs. 772-773) and three cases with three such bodies at various distances (figs. 774-776). Other sketches on the same folio (figs. ) make explicit the camera obscura-eye analogy and leave no doubt concerning the parallels intended between physics of light and shade and physiology of vision.

9. Shape of Aperture

When light passes through an aperture does the resulting image on the wall resemble the shape of the aperture or the light source? Already in Antiquity this had been a problem as is evident from two questions posed in the Problemata attributed to Aristotle:

Alhazen, in the eleventh century, had mentioned the problem of light passing through apertures.¹³ Witelo, in the thirteenth century had considered briefly light passing through square, round and angular apertures.¹⁴ With Pecham this phenomenon emerged as a serious problem. He devoted two of his longest propositions to the properties of images passing through triangular apertures.¹⁵

Leonardo sands clearly within this tradition. A diagram on A 82v (fig. 778, 1492) bears comparison with standard diagram from Pecham's work (fig. 777). But whereas his predecessors had been content to consider isolated cases, Leonardo is more systematic. In his notebooks he illustrates a series of situations showing how, with greater distance, the image gradually loses the shape of the aperture and takes on the shape of the light source. When the light source, aperture and projection plane are very close, the light passing through a triangular aperture produces a triangular image. This limiting case (fig. 783) he considers in some detail a situation in which a triangular image begins to become curved (figs. 780-782, cf. fig. 779):

The exterior sides of compound derived shade are always seen by all the luminous body.

But if the angle is convex then the impression of the obtuse angle will make an acute angle.

(Figs. 783-788: Stages in the transformation of a triangular image to a round image. Fig. 783, Author's reconstruction: fig. 784, CA277va; fig. 785, C10v; fig. 786, Forst III 29v; fig. 787, H227 inf. 50v-51r; fig. 788, H227 inf. 49r.

How the shadow of an obtuse angle makes itself acute with curved sides.

As the distance increases each point of the triangle generates a circle in the form of the light source which results in a triangular configuration of three circles. He illustrates this situation on CA277va(fig. 784, 1508-1510). On C10v (1490-1491) he shows (fig. 785) a next step in this process where the circles have begun to overlap. The accompanying text summarizes the phenomenon:

On Forster III 29v (fig. 786, c. 1493) he demonstrates a next stage in this process of transformation. The distance is now greater and the three circles have begun to overlap more. The accompanying text is brief: "The angle is terminated in a point. In the point are intersected the images of bodies." A next stage, where the distance is greater and the circles overlap even more is recorded on Manuscript H 227 inf. 50v-51r (fig. 787) accompanying which is a thorough explanation:

When the distance is greater still the image takes on entirely the shape of the original light source and is fully round, in spite of having passed through a triangular aperture.¹⁶ This situation he describes in draft on CA135va(1490-1492) and develops on H227 inf. 49r (fig. 788):

CA135va H227 Inf. 49r

The further from the intersection The further from the intersection

/that/ the second pyramid /is/, ...that the base of the second

the more it expands at the object. pyramid made the object is

Its circles created at the angle generated, the more it expands.

of the aperture enter more into And its circles created in the

the body (the one than the other) angles of the apertures are

and to the extent that they incorporated together more, and

incorporate one another, the more the more that they are incorpora-

the solar ray remains round at ted together, the rounder the

the object. base of the solar pyramid remains.

When the rays have made so long a

path that they enter four hundred times

into the greater diameter of the

aperture, the rays will carry to the

object a spherical body and the form

of the aperture will be lost.

Given his interest in the light-sight analogy (see above pp. ) it is not surprising to find him on H71 /23/(r) (fig. 790, 1494) examining what happens when an eye looks through a triangular aperture. "The eye," he concludes, "does not comprehend the nearby luminous object." He is equally interested in the properties of square apertures and occluding objects. On C12r (1490-1491), for instance, he (fig. 791) asks: "What shadow a square umbrous body will make with a spherical luminous source?" On A20r (1492) he notes how: "the solar rays repercussed on the square mirror will rebound in a circular form on the distant object." On CA256rc(c. 1492) he considers a variant situation in which (fig. 792) a rectangular light source passes through a circular aperture and projects a rectangular image.

When a circular light source, a square aperture and a projection plane are close to one another, the projected image takes on the squareness of the aperture. This limiting case (fig. 793) Leonardo does not illustrate. As the distance increases each of the four corners of the aperture generates intersecting circles. This situation he illustrates (figs. 794-797) and describes at length in a passage recorded on H227v inf., 48r-48v:

The passage ends with a description of what happens when the distance is increased:

Which /circles/ in going a long distance are lost because they are converted to darkness and thus P, K, L /and/ O become rounded and complete the spherical body and finally over a long distance the square E is converted to a circle and all the other parts of less duplicated light are lost.

How these circles gradually come together as the distance increases he sketches roughly on CA135va (fig. 798, 1492), and then with more care in a diagram recorded on H227 inf. 48v (figs. 799-800) accompanying which he writes:

Proof in what way the square is made in the form of a sphere by the solar rays at the object.

This description of how a square is transformed into a circle effectively provides a visual demonstration of the age old problem of quadrature of the circle. Which raises the question: did Leonardo perhaps see in these optical experiments a case study in principles of practical geometry? This would, for example, account for a striking resemblance between the diagrams (figs. 795-795) just analysed and a diagram on Forst II 5v (fig. 794, c. 1495-1497), above which he writes "True proof of the square" and below which he adds:

Whether or not he saw these connections with transformational geometry, he was clearly fascinated in studying various stages in the process of a square image becoming round. On CA135va (fig. 798, 1492), for instance, he records a further stage in which the four circles nearly overlap one another completely. Accompanying this he drafts another passage which again emerges in more polished form on H227 inf. 49r (fig. 799):

CA135va H227 inf. 49r

It is a necessary thing that the It is a necessary thing that the

intersections of...round intersection of the round pyramid

pyramids is made in a single is made in a single closed point

point which is closed...of a of a non-transparent circumference.

non-transparent circumference. Therefore the half-round pyramid

It is necessary that the inter- will divide the point only

section made by the half-round surrounded by the half part, which

pyramid is amde in a point point you will find in the right

closed only...by the half part. angle and if you approach it to

the angle of the eye it will

appear to you in the form of a

half-circle.

On H227 inf. 50v (fig. 800) he considers a case where the distance is greater still and the image becomes completely round, losing all trace of the square aperture:

Of luminous bodies.

An understanding of this phenomenon how the image of a round light source passing through a square aperture is square at a close distance and round at a greater distance helps us, in turn, make sense of a passage on A64v (1492) that is puzzling if read out of context:

(Every aperture carries its form to the object over a long distance.)

Having considered the characteristics of triangular and square apertures, he explores slit-shaped apertures. On CA135va (1492), for example, he draws (fig. 802) a case where each of the two end-points of the slit produces a circle. He then redraws the slit (fig. 803) showing how the two circles overlap more at a greater distance. These diagrams are without text. When he pursues the problem on H227 inf. 51r-51v (fig. 801) he adds an explanation:

On CA135va (fig. 804, 1492) he also sketches a related case where two rectangular faces are positioned such that they produce an open slit. This he again draws and describes on H277 inf. 51r-51v (fig. 805):

On A64r 91492) he sketches (fig. 806) and comments briefly on another variant in which one slit is placed above another: "It is impossible that the luminous rays which have passed through parallels demonstrate to the object the form of their cause." On CA135va (1492) he sketches yet another variant in which the two slits are side by side (fig. 807). This he develops on H227 inf. 49v (fig. 808), explaining:

Having placed the two slits above one another and beside one another Leonardo explores the next logical combination in which the two slits intersect one another to form a cross-shaped aperture. On C9r (1490-1491) he illustrates (fig. 809) and describes a case where light source, aperture and projection plane are near one another, with the result that the image resembles the aperture:

The luminous ray which has passed through a small aperture and the stamp of its percussion having been interrupted at a nearby opposition will be more similar to the aperture...through which it passes than the luminous body whence it originates.

On CA135va (1492) he sketches how each of the ends of the cross shaped image acquires a rounded shape (fig. 810). Next he shows how, at a greater distance, four circles emerge (fig. 811) which, at a greater distance still overlap more (fig. 812). Accompanying this he indicates the distances involved in quantitative terms:

The transit of solar rays through an angular aperture is necessary in some space.

On H227 inf. 49v 49v-50r, he illustrates (fig. 813) a situation where the distance is more than 30 braccia and the four circles are nearly coincident with one another. This he discusses in detail beginning with a general statement:

A specific description of the diagram (fig. 813) follows:

At a still greater distance the image loses all trace of the cross-shaped aperture and becomes perfectly round like the light source. This situation he demonstrates (fig. 814) on C10v (1490-1491) beneath which he adds:

Leonardo has analysed in detail the properties of images passing through apertures in the form of triangles, squares, slits, double-slits and crosses. But he is not content to stop here. On C7v (1490-1491) he alludes to a more complex situation:

Perspective

Accompanying this he sketches in rough form an eight sided star (fig. 819). The problem is not forgotten. Within two years he describes this eight-sided star at length in connection with eight apertures on CA187ra (c.1492):

Remember that you note the quality and quantity of the shadows.

This entire description is written in the margin surrounding a carefully drawn diagram beneath which he writes: “This shadow is made by a spherical umbrous body illuminated by a light made in /the form of a/ star, which has its rays of equal size.” In the lower right-hand part of this folio he has drawn (fig. 837) a draft of this octagonal star shaped aperture. Directly above this are four intersecting circles such as would result from a square aperture (fig. 815, cf. figs. 794-797). Beneath the principal diagram showing the shadows produced by the octagonal star (fig. 838) are three other diagrams of intersecting circles: two circles, as would result from a slit (fig. 816, cf. fig. 803), three intersecting circles, as would result from a triangular aperture (fig. 817, cf. figs. 784-785), and four intersecting circles as would result from a cross-shaped aperture (fig. 818, cf. figs. 811-812). In short, this octagonally shaped aperture marks the culmination of a series of experiments.

CA241rd.

On CA256rc (c.1492) he drafts a summary of these results: "In the percussion of rays is demonstrated part of the nature of its cause." Which idea he then reformulates in a passage headed:

On the nature of apertures

10. Number of Apertures

If we return to read more carefully the passage on CA187ra (c. 1492), we find that he not only mentions an eight-sided aperture, but also eight apertures equidistantly arranged in a circle. This is not an oversight on his part. For just as he has been studying the properties of multi-sided apertures, so too has he been exploring the comparable properties of multiple pinhole apertures. On CA277va (1508-1510), for instance, where he outlines his new plan for arranging the work on light and shade (cf. Chart 10 above), he illustrates the image cast by one pinhole aperture (fig. 822), two (fig. 824), three (fig. 829), four pinhole apertures (fig. 834), and a rough sketch with the image cast by perhaps as many as eight pinhole apertures (fig. 838, although this could well represent an advanced stage in the rounding produced by three apertures, fig. 830, cf. 831).

These draft sketches on CA277va (figs. 822, 824, 829, 1508-1510) are developed on CA241rd (figs. 823, 825, 836, 1508-1510), this time accompanied by text. In the upper right-hand margin he notes in passing: "Many minimal lights in the long distance will continue and make themselves noticeable." In the main body of the text he drafts general rules of light and shade (see below, p. ). Alongside the drawings he discusses the:

Nature of the light which penetrates apertures.

Having answered his first two questions he considers the proportions of light involved under the heading:

Of the proportion that the impressions of light have placed partly one above the other.

To demonstrate this he now describes his figures (figs. 823, 825, 835, 836):

Further examples of four apertures occur on CA177rb (fig. 833); CA177vc (fig. 840, 1508-1510) he makes a rough sketch involving perhaps as many as eight apertures. On CA187ra (cf. fig. 838, 1492) he explicitly describes the use of eight apertures and on CA385vc (fig. 841, 1510-1515) he carefully draws apertures and the eight circles thereby produced. On the same folio he sketches two other cases with 18 apertures (figs. 842-843). This theme of multiple apertures is developed on CA241vc (1508-1510). Here he draws three intersecting circles which frame 24 apertures (figs. 845). Beneath this he draws another diagram (fig. 846) with 24 apertures to show how these, at a greater distance, produce 24 interlacing circles. Accompanying these diagrams on CA241vc is a text that develops the ideas of CA241rc:

D

On light

This leads to a second general rule:

Of multiplied brightness taken from a single luminous body.

And this is proved in the 3rd, behind this face, etc.

On CA229vb (1505-1508) he takes this theme further. He begins with a rough sketch showing two circles inscribed within a larger one (fig. 847): this might represent a situation involving two apertures. He then draws (fig. 848) four apertures and the four circles thereby produced. There follow other examples which are multiples of four, beginning with a sketch (fig. 849) of 16 (4 x 4) apertures with a hint of the circles they produce. Next he draws (fig. 850) 12 points on a half-circle, which would amount to 24 (4 x 6) apertures in all. A case (fig. 851) involving 21 (4 x 7) apertures follows. Finally he draws (fig. 852) a series of eight circles which span but a quarter of the circumference of a circle that would contain 32 (4 x 8) apertures. Of these various examples only the case involving 28 apertures (fig. 851) is accompanied with a text:

We have already noted Leonardo's implicit comparison between multiple sided apertures (triangles, squares, crosses, octagons) and multiple-apertures (1, 2, 3, 4, 8, 16, 24, 32 pinholes). On looking more closely at CA229rb, vb as a whole another, theme of comparison becomes apparent: he is analysing multiple-apertures on the same folio that he is exploring multiple shadows produced by a St. Andrew's cross.

This is not a coincidence. His analyses of the multiple shadows produced by a St. Andrew's cross occur on CA37ra, 177rb, 177ve, 241rcd, and CA229rb, vb (see above pp. ). These are the very folios on which he also explores multiple aperture problems of light (see Chart 18).

CODEX MULTIPLE APERTURES MULTIPLE-SIDED MULTIPLE

APERTURES SHADOWS

CA177rb 4 4

CA177ve 4 6

CA241rcd 1, 2, 3, 4 2, 4

CA241vc 24 1 (on multiple

surfaces)

CA229rb,vb 4,16,24,32 2,4,6

CA277va 1,2,3,4, 3 1

CA37ra 1 (in various degrees) 2,4,6

CA385vc 8, 18 1,2,3,

CA187ra 8 2,3,4,8 2,3,4,8

11. Apertures and Interposed Bodies

We have examined how Leonardo explores the properties of light when it passes through apertures of various shapes such as slits and crosses. A next stage in complexity would be to study such apertures in combination with various shaped opaque bodies. This he does on CA187va (c. 1492) where he makes a series of preliminary sketches to show what happens when light passing through a slight-shaped opening encounters a spherical object (figs. 853-854, 856-862). Above these diagrams he makes two drafts of an explanation:

Unsatisfied, he crosses out these drafts. He turns the sheet ninety degrees and makes two further sketches showing how light, having passed through a slit, and encountering a spherical object, produces a combination of simple and mixed shadow (figs. 855, 864). In the left-hand margin he drafts a phrase: "That light which," then stops short. Alongside the lower diagram he notes: "This light is long and then." Directly beneath this he writes: “No separate shade can stamp on the wall the true form of the umbrous body, if the centre of the light is not equidistant from the extremities of this body.” In the upper left-hand margin he now claims:

On CA187ra (1492) he redraws his sketch of light passing through a slit, which encounters a sphere and casts shadows on the wall (fig. 863). Alongside this figure he writes: "Remind yourself that you note the qualities and the quantities of the shadows." On A89v (BN 2038 9v, 1492) he redraws the situation (fig. 865) and on A89r (BN 2038 9r, 1492) he develops it into a beautiful diagram without text (fig. 866). As is so often the case, he expects that his visual statement will speak for itself.

Closer attention to the other sketches on CA187ra (1492) again reveals Leonardo's delight in playing with variables. Having shown what happens when a slit-shaped light encounters a spherical opaque body (fig. 863), he considers what occurs when a spherical light encounters a slit-shaped opaque body (fig. 867). Not content to stop here he lets light pass first through a round and then through a slit-shaped aperture (figs. 868-869) and contrasts this with light which passes first through a slit-shape and then through a round aperture (fig. 870). Next he replaces this slit-shape with a cross shape (figs. 871-875).

This final example can be seen as a starting point for his illustration more than fifteen years later on CA207ra (fig. 876, c. 1508-1510) to "make a crucifix enter a room." Here he takes a blank wall on which he marks a crucifix. Opposite this wall he positions an aperture which is in a room. The sunlight reflects the light of the wall, enters through the camera obscura and casts the image of a cross into the room, (cf. Kircher's later example, fig. 877).

A more complex play with cross-shaped images is suggested on Triv. 22v (fig. 878, 1487-1490) which may be the basis of his diagram on C11r (fig. 879, 1490-1491) where light passes through a cross-shaped aperture, encounters a transparent sphere and then casts a rounded cross-shaped shadow. Accompanying this he notes:

In 1508 he returns to this problem of cross-shaped images, now in an unexpected context. On F28v (fig. 880) he observes that:

By way of illustration he makes two sketches to show how smaller bubbles¹⁷ surrounding the larger bubble (figs. 881-882) might serve to generate a cross-shape. On CA236rd (1508-1510) he makes a note: “on the shadows situated at the bottom of the water and which send their species to the eye through water and through the air,” but precedes to discuss refraction (see below p. ). He appears not to have pursued the problem of cross-shaped bubbles as he had hoped.

In the period 1508-1510 he does return, however, to problems of slit-shaped apertures and opaque bodies on CA258va. Here he begins (fig. 883) with light passing through a slit-shaped aperture which encounters a narrow opaque body and casts a shadow on the ground at ninety degrees to this. Directly beneath he explains:

Next he considers a situation where this shadow is cast at more than ninety degrees (fig. 884):

Immediately following he turns to the converse:

There follows the converse of the said.

To illustrate this he moves an interposed stick through various degrees of obliquity (fig. 885). Finally he considers a case where a slit-shaped aperture, thin opaque body and the resulting shadow are all in the same plane (figs. 886-887)

This situation interests him and on CU630 (TPL627, 1508-1510) he examines it in more detail under the heading:

Of the derived shade created by light of a long shape which percusses an object similar to it.

A specific demonstration follows (fig. 888):

Having studied in isolation the effects of different shapes of umbrous bodies and apertures, he examines various situations where these factors act in combination. On C9v (1490-1491), for instance, he draws a light source (fig. 889) the rays of which, on meeting an opaque body, cast a shadow which passes through an aperture. On the far side of this aperture are two further light sources g and h which cast rays intersecting this shadow. Directly beneath this diagram he adds a brief text:

On W12352v (c. 1494) he draws another diagram (fig. 890) of a luminous body the rays of which meet an opaque body and cause shadows which then pass through an aperture. Here there is no accompanying text. But then on CA236rc (1508-1510) he redraws the diagram carefully (fig. 891) and adds a full explanation under the heading:

What difference there is between shadow and image.

Meanwhile, on CA216rb (c. 1495) he had been exploring more complex variants of this situation. In a first diagram (fig. 892) a light source is left undrawn and an opaque object casts its shadow through two apertures onto a wall. In a second diagram (fig. 893) there are again two apertures, but now there is an opaque body in front of these apertures and a smaller opaque body behind them. Their shadows combine to produce a series of four intersecting circles. Finally there is a third diagram (fig. 894) which has the same elements and differs only in that relative sizes of the opaque bodies are changed. There is no text accompanying these diagrams.

On CA238vb (1505-1508) he takes a flat rectangular board and a round ball. These he places in near proximity to one another in order that they effectively function as an aperture. He then examines the effects produced by moving the light source and altering relative positions of the board and ball. Accompanying the series of diagrams that result (figs. 895-963) he drafts a number of only half intelligible notes which are here translated without comment:

All [fig. 901] the luminous rays that are cut by n are lacking at m.

(The umbrous body outside the window)

(The solar rays)

(Here the shadow of the board carried by solar rays).

Of which it happens (that the)

(Here) many correlates, that is derivatives.

(Here the...solar rays which terminate the shade)

Of the circle.

The umbrous body inside the window, the sun always....

ae [fig. 897] is the lower limit of the shadow of the board.

Related diagrams are to be found on CA238rb (figs. 712-719, 1505-1508) and CA133va (figs. 904-909, 1497-1500. With two exceptions these are without text. Beneath one (fig. 908), he points out that "the line ab is the boundary of the luminous body." Below the largest diagram (fig. 909) he writes: "When n touches m, f will touch g." On such folios which represent an interim stage int eh development of his ideas, rough sketches suffice. Careful explanation is not yet necessary.

12. Spectrum of Boundaries

Leonardo's studies of a camera obscura in combination with opaque bodies lead him to abandon his early assumptions concerning clearly defined boundaries and to emphasize instead a spectrum of gradations between light and shade. This he does in terms of demonstrations involving a series of basic arguments: (1) that derived shade has less power to the extent that it is more distant from its primitive shade; (2) conversely, that derived shade has more power when it is closer to its source; (3) to what extent one can speak of uniformity of derived shade; (4) that primitive and derived shade mix with distance; (5) where primitive and derived shade are joined together; (6) where shade is greater; (7) where primitive and derived shade are not joined; (8) implications for the perception of backgrounds and (9) simplified gradations of shade.

We shall consider his demonstrations for each of these arguments in turn and show how these interests lead directly from the physics of light and shade to problems of vision and perception.

12.1 Derived Shade is Less Powerful When More Distant From Its Primitive Shade

The idea that derived shade loses strength with distance is clearly expressed on CA258va (1508-1510):

He mentions this idea in passing on CU705 (TPL553d, 1508-1510): "The darkness of the derived shade diminishes to the extent that it is more remote from the primitive shade." On CU707 (TPL561, 1508-1510) Leonardo returns to this problem in greater detail in a pass age entitled:

On compound derived shade.

A concrete demonstration (fig. 924) is cited in support:

12:2 Derived Shade is More Powerful When Closer to Primitive Shade

On CA144va (c. 1492) he drafts this idea:

This he crosses out. On CU730 (TPL598, 1508-1510) he takes up this claim afresh under the heading:

Whether the derived shade is darker in one place than in another.

He reformulates the idea on CU699 (TPL606, 1508-1510) under the heading:

Of the boundaries of derived shade.

Immediately following the objects of an adversary are mentioned and answered:

12.3 Uniformity of Darkness

The above two demonstrations serve as basis for his comments on CA258va (1508-1510):

On the Uniformity of Derived Shade.

12.4 Primitive and Derived Shade Mix With Distance

The concept that primitive and derived shade mix with distance is implicit in a statement on CA256rc (c. 1492): “To the extent that the umbrous body is closer to the percussion of the rays its shadow will observe the form of its derivation more.” On CA144va (c. 1492) he drafts an idea: “(That part of the derived shade will mix itself less with its boundaries in the light that surrounds it which is closer to the primitive shade.)” This he crosses out and makes two further drafts:

One reason for this claim stems from everyday experience as is clear from a passage on A92v (BN2038, 2v, 1492): “How the shadows are confused over a long distance is proved in the shadows of the moon which are never seen.” On CU636 (TPL438a, 1505-1510) he returns to the general problem in passing: "and the derived shade mixes itself the more with the light to the extent that it is more distant from the umbrous body." Which idea he reformulates on CU699 (TPL606, 1508-1510): "That shade is more distinct and defined which is closer to its origin, and the more distant is the least defined," and on CA371rb (1510-1515) he expresses it differently again:

12.5 How Primitive and Derived Shade are Joined Together

Related to the foregoing is a demonstration on CU697 (TPL562, 1508-1510) entitled:

How primitive and derived shade are joined together.

By way of illustration he gives a concrete example (fig. 925):

This theme he pursues on CU708 (TPL563, 1508-1510) headed:

How simple shade is conjoined with compound shade.

A demonstration without an illustration follows: “This is proved and let the luminous body body be abc and the umbrous body de and let the simple derived shade be def and let the compound derived shade be fek.” And leads to a second claim: “But the compound derived shade always sees a part of the luminous body, greater or less, depending on the greater or lesser distances that its parts have from the simple derived shade.” Which, in turn, is demonstrated, again without an illustration:

12.6 Where the Shade is Greater

On Forst III 87v (c. 1493) Leonardo mentions how the extremities of shade are affected by light:

The luminous or illuminated object bordering on the shade intersects as much as it cuts.

On H66/18/(r) (January 1494) he notes: "that part of the derived shade will be less dark which is more distant from its extremities." He returns to this idea in two drafts on CA190rb (1505-1508):

On this same folio he also drafts another phrase: "That object will make itself darker which is...seen by a greater amount of darkness." The way in which this and related themes are associated in Leonardo's mind is seen clearly on CA230rb (1505-1508) which opens with a series of general claims and a questions:

The boundaries of the maximal derived shade is darker than its middle.

The surface of every opaque body participates in the colour of its object.

Why shades tinge dense bodies and not rare ones?

This is followed by a further question: “Why the shadows intersected behind the maximal shade, lose more darkness to the extent that they approach such a maximal shade?” This is answered with the help of a demonstration (fig. 911):

The accompanying diagram (fig. 911, cf. figs. 910, 912) recalls his studies of divergent shade (see above pp. ). Above this diagram he adds a brief caption: "To the extent that g /and/ i are less, to that extent are the whites surrounding maximal shade narrower." To the left of this he draws a further diagram (fig. 913, cf. figs. 912, 914-915), beneath which he explains:

Which explanation continues in the next column to the left:

He restate this conclusion in passing on CU699 (TP606, 1508-1510); "The shade will show itself as darker towards the extremities than towards its centre," and sets out to demonstrate it afresh on CA195va (fig. 930, c. 1510):

And in their boundaries colours are more intensive and brighter than their parts.

Later on the same folio he pursues this theme asking (fig. 930):

CA297va.

First reply.

Such investigations lead him to examine precisely where gradations of light and shade are brighter or darker. On CA297va (1497-1500), for instance, he makes a preliminary sketch (fig. 916) which he then redraws (fig. 917) and describes:

And the 3rd line pq sees the entire umbrous body cp and all the luminous body ac.

Roughly a decade later he takes up this theme afresh on CA37ra (1508-1510). He now draws two preliminary diagrams (figs. 918-919) and then a third (fig. 920, cf. figs. 921-922). As usual, the accompanying text opens with a general statement:

CA277ra.

A demonstration follows (fig. 920):

He now writes a new heading: "Of the middle contained by the extremities." He is, however, unsatisfied and crosses out the entire passage. In the right-hand margin he begins afresh:

This divides itself into 4: 1st: of the extremities containing the compound shade.

2nd: of the compound shade within the extremities.

Again he breaks off and in the lower centre of the folio he notes in passing: "Where the shade is greater or less or equal to the umbrous body, its origin." He now turns the folio to the side, draws a considerably more complex diagram (fig. 923) and analyses it in a passage headed:

Of the shade bch.

He pursues this theme of various gradations of brightness and darkness on CA258va (1508-1510) beginning with two demonstrations (figs. 956):

An interim paragraph follows in which he introduces the question of maximum brightness.

To this end a further demonstration follows:

He returns to this theme on CU669 (TPL719, 1508-1510) under the heading:

and fig. 927, K/P 178r.

Of the brightness of derived light

The diagram for the demonstration that follows is reminiscent of earlier discussion in this context (fig. 926, figs. 924-925):

And through such a discourse we have proved that r is the brightest part of the pavement qs.

12.7 Where Primitive and Derived Shade are Not Joined

On CA258va (1508-1510), having discussed conditions under which primitive and derived shadow are joined he considers (fig. 928):

Of the shadow that does not join the derived and the primitive.

A similar diagram and demonstration are found on CA195va (fig. 929, 1508-1510) where he observes:

These diagrams are the more interesting because they return to a problem that had perplexed him in his earlier studies of light and shade, namely, what causes the shadow of an opaque body smaller than the light source to be divergent. On CA195va (1510) he draws (fig. 930, cf. 931) a camera obscura in which the entering light encounters two opaque bodies and produces complex gradations of light and shade, which he describes briefly: “op sees and is seen by ab and is tinged by its colour and on the side p is seen the beginning of the brightness of the air which brightens the place where its image percusses.” Hence this combination of camera obscura and opaque objects provides yet another demonstration for his "colour participates" argument (see above pp. ).

12.8 Implications for the Perception of Backgrounds

At the same time this demonstration serves as a starting point for a further argument.

This particular demonstration is of considerable interest because, as will be shown (see below pp. ) he had made various experiments to establish the contrary, namely, that, white on a black background appears whiter and black on a white background appears darker. On this same folio he explicitly compares the effects of a camera obscura with those of the pupil in the eye. Problems relating to physics of light and shade, the physiology of vision and perception are all intimately connected in Leonardo's mind. As a result what had traditionally been philosophical and psychological questions of vision and perception now emerge as problems of physics. Problems of optics are no longer a matter of theoretical debate but open to practical verification by experiment. He returns to this situation of a sphere placed within a camera obscura once more on W19086r (K/P178r, fig. 927, c. 1513) where he notes that:

12.9 Simplified Gradations of Shade

Parallel with these demonstrations is a further series, which omits the interposed opaque sphere and reduces the problem of gradations of shade within the camera obscura to its essentials. Preliminary drawings (figs. 932-941) on this theme are found on CA345rb (1505-1508) amidst discussions of species being everywhere in the air (cf. pp. ) and how things cannot be seen without apertures (cf. pp. ). Among these ten drawings, only one is explained (fig. 941):

On CA190rb (1505-1508) this theme of gradations of light/shade within a camera obscura is developed. In the right-hand column he begins with a preliminary sketch (fig. 942), beneath which he draws a camera obscura with various gradations (fig. 943). To this diagram he adds six letters. These, however, are not explained. Beneath the diagram he merely notes: "That object will be darker which is seen by a greater sum of darkness." He now draws two further diagrams showing gradations of shade in a camera obscura (figs. 944, 947) and in the passage that follows describes the one on the right under the heading:

A precise description of the figure now follows:

Here the right-hand column ends. In the upper left-hand column he drafts two further diagrams (figs. 945-946) beneath which he drafts an explanation of the left-hand figure:

Here his manner of referring to different fractions of light and shade strikes us as familiar. We have encountered it on more than one occasion (see above pp. ). His references to maximal light and shade we have also encountered elsewhere (CA258va, CA230rb, CA345rb). But if the initial thoughts remain similar, their applications are, nonetheless, quite different. This diagram in the upper left-hand margin is probably a draft for the left-hand diagram (fig. 947) in the right-hand column, which he describes after he has crossed out his draft:

Why the derived light that passes through an aperture into a dark place does not make percussion of uniform brightness.

Here the text breaks off and he gives instructions to turn the "page" to CA190vb (1505-1508) which opens:

O mathematicians throw light on such error.

This is reminiscent of a passage on CA345 (see above pp. ), which also occurs in connection with a camera obscura passage. The lower part of CA190vb contains various diagrams relating to the inversion of images within the eye (figs. ) to be discussed later in section three. Amidst these diagrams he draws another preliminary sketch of a camera obscura with its gradations of shade (fig. 948), beneath which he draws two more elaborate versions (figs. 949-950), the latter of which appears intended to serve as an imitation eye. Alongside this figure he adds a text which is interrupted:

Here the transition from physics of light and shade in a camera obscura to problems of vision and perception remains implicit.

13. Camera Obscuras and The Eye

On D10v (1508) this analogy is taken one step further. Here towards the centre of the right-hand column he draws a camera obscura with various gradations of shade (fig. 951). Above this he writes: "first." Above this, in turn he draws an eye in which various rays are being inverted at the pupil (fig. 952). This figure is headed: "second." Between these two figures he adds a brief marginal note: “The boundaries of bodies are little known because such boundaries are made in surfaces reduced to lines which being indivisible are imperceptible.” Lower down the same right-hand column this perceptual problem is pursued:

Here the bridge between Leonardo's physics of light and shade and his physiology of vision is manifest. Indeed it is clear how his camera obscura studies which make him aware of differing gradations of light and shade influence both his theories of perception and painting. Leonardo returns to these themes briefly on CA195va (c. 1510) which, as has been noted, is another of those folios on which the camera obscura-eye analogy is explicit (see above pp. ). In the lower left-hand portion of this sheet is a rough sketch (fig. 953) of a camera obscura with five gradations. In the lower centre is a slightly more developed version (fig. 954) with seven gradations and near the bottom is an example with nine gradations (fig. 955). Each of these three possibilities is duly recorded in a brief note: "Make five or 9...or 7 spaces in ir in order that the white no stands in the middle." Beneath this is a further passage which partly explains the bottom diagram (fig. 955):

Even if this text is interrupted, the accompanying diagrams remain of considerable interest because they reveal that Leonardo is trying to quantify gradations of shade. He wants, as far as possible, to measure what had previously been a purely subjective problem and thereby he brings the field of optics one step closer to its modern position as a branch of mathematical physics.

14. Conclusions

Although it is generally known that Leonardo worked with the camera obscura and compared the inversion of images in this instrument with those of the eye, scholars often refer to these facts as if they were only mentioned in passing in the notebooks. Our comprehensive study of the topic has shown that Leonardo devoted no less than 270 diagrams to the theme of camera obscuras and that these interests grow in part out of the astronomical tradition. He uses the camera obscura to demonstrate not only the inversion of images, but also that images passing through an aperture do not interfere with one another, that images are all in all and all in every part, that pinhole apertures produce different intensities of light and shade and that inverted images demonstrate a contrary motion.

Mediaeval optical writers had given considerable attention to the images of round light sources passing through triangular and other complex apertures. Leonardo studies the problem systematically in the case of triangular, square, octangular, slit-shaped and cross-shaped apertures. He demonstrates that whether the shape of the projection resembles the aperture or light source depends on the relative distance of these factors. He does not attempt to arrive at a formula for these relationships but he does give some quantitative references to his experiments.

In addition he studies situations with 1, 2, 3, 4, 8, 16, 24 and 32 pinhole apertures. He also studies the effects of light, which passes through apertures of different sizes and encounters various interposed objects. Such experiences lead him to new studies of gradations of shade which prompt further analogies with problems of visual perception: why, for instance, the eye cannot perceive clearly the boundaries of nearby objects.

The great importance of these extensive studies of the camera obscura is that they bring various questions concerning the nature of light and shade and vision into the experimental domain of physics. Optics is no longer a problem for philosophical discussion: it is now a domain which requires scientific demonstration. In the section that follows we shall see how this mentality also leads Leonardo to make physical models of the eye. If the answers he finds are not always correct, the new kinds of answers he seeks are nonetheless important.

Notes

1. Leonardo ↩︎
2. Leonardo ↩︎
3. Leonardo ↩︎
4. ↩︎
5. Levi ben Gerson ↩︎
6. Alhazen ↩︎
7. Witelo ↩︎
8. ↩︎
9. Leonardo ↩︎
10. Missing Citation ↩︎
11. Missing Citation ↩︎
12. William of St. Cloud ↩︎
13. Alhazen ↩︎
14. Witelo ↩︎
15. Pecham ↩︎
16. Missing citation ↩︎
17. Missing Citation ↩︎