Dr. Kim H. Veltman
The Structure of Manuscripts F and D
2. Manuscript D
3. Manuscript F
In the Middle Ages optics and astronomy became ever more closely linked (see above pp. ). Among the Arabs Euclid's Optics became required reading for a study of Ptolemy's Almagest.1 Optical writers such as Roger Bacon, developing Aristotle's ideas suggested that the twinkling of stars was due to deception within the eye2 and that the apparent size of the moon and other planets was a result of refraction in the atmosphere.3 By the fourteenth century, Dante, in his Convivio, could go further and describe astronomy as if it were a branch of optics:
The site of these mobile heavens is manifest and determined by an art which is called optics (prospettiva) and by arithmetic and geometry and is reasonably seen also by other sense experience.4
Leonardo takes further this subordination of astronomy to optics. He believes that the twinkling of stars is caused by rays of light reflected by the eyelids. He studies the paradox that a more distant light source may appear not to diminish in size and decides that this can be accounted for by changes in pupil size. Since such deceptions concerning heavenly bodies have their origins in the eye, an analysis of the visual process becomes necessary for a study of astronomy. In Manuscript D, he examines the entire visual process: how images reflect from the eyelids, pass through the cornea and pupil, the lens and interior of the eye to the optic nerves and finally to the brain. In the Manuscript F, by contrast, he concentrates on the role of eyelids, cornea and pupil in looking at stars, but does not mention the inner workings of the eye.
There are other basic differences between the two treatises. Manuscript D has as many as four drafts for a single demonstration. Manuscript F is more coherent. In Manuscript D astronomy is mentioned on a single folio. In Manuscript F it is mentioned repeatedly. Nonetheless, as will emerge later, both treatises constitute drafts for a work on optical astronomy. Leonardo's chief treatises on vision have an ulterior motive.
2. Manuscript D
Manuscript D is entirely devoted to optical problems and hence it is commonly assumed to be a coherent treatise. It is, in fact, an advanced draft, or more precisely, a series of advanced drafts. Strong (1967), in his analysis of the treatise has drawn attention to the headings of the folios which, as he has astutely noted, fall into two groups: 1) those headed "On the eye" and 2) those entitled "On the human eye" or "On the eye of man."5 It bears adding that the two groups also deal with basically different problems. Six of the eight pages headed "On the eye" deal with the eyelids and cornea. In the second group all twelve pages concentrate on what happens to images on passing through the pupil, the lens, humours and the optic nerves. Hence passages headed "On the eye" deal with the outer eye, while those headed "On the human eye" or "On the eye of man" deal in particular with the inner eye (see Chart 27).
It is tempting to assume, as does Strong,6 that one can reconstruct the sequence in which Leonardo wrote these two drafts. Unfortunately, Strong's reasoning, however convincing, leads to a confusing arrangement (see Chart 28). For it would mean that Leonardo opened his discussion of the eye with the cornea and then devoted a page in turn to eyelashes, inner eye, cornea, eyelashes, inner eye and cornea. The proposed arrangement of the second group, while more coherent, is also inconsistent.
Chart. 27. The contents of Ms. D are compared with Leonardo's page headings.
A logical treatment of the visual process would trace the course of an image from a position outside the eye, through the cornea, pupil, humours and optic nerves. Such an approach would impose a quite different structure on Manuscript D. The treatise might then begin with a general statement concerning visual power and its relation to the other powers of nature on 1r and a general consideration of the eyelids on D1v, which ends with the note: "Now such a demonstration such as this should be divided into its parts to make it better known, placing first its conceptions and other propositions necessary for a similar proof etc." Such a treatment of the eyelids occurs on 9v. A next theme would be the position of objects on the surface of the eye which he treats on 2r and then in more detail on 10r, followed by a consideration of the cornea on 7r. Assuming that all the passages headed "on the eye" were written in sequence then 7v which deals with the uvea and 10v, which considers the whole visual process, would have ended the first group.
In a strictly logical arrangement the passage on the cornea on D7r would have been followed by a discussion of pupil size: first hypothetical cases in which the pupils are larger than life (6)r; then a comparison of pupils in various birds and animals (5v and 5r) and finally changes in human pupil size (4r).
|8v||Visual Field, Inner Eye|
Chart 28. Sequence of folios in Manuscript D according to Strong.
On 4r he considers the perception of an object smaller than the distance between two eyes and on 9r, the perception of smaller objects. This would lead to demonstrations which use the perception of such small objects to confirm that images are all in all and all in every part (6v, 2v, and 4v). On 7v he gives preliminary instructions concerning a model eye, which he then develops on 3v, where he also considers alternative paths of images in the eye., This theme he pursues on 3r, where he draws alternatives which he personally does not accept. On 8v he draws what he considers to be a correct path of the rays within the eye and returns to the problem of the central ray. On 8r this path of the rays is red rawn with greater care. He now notes that the width of the rays on leaving the crystalline lens is 1/3 of its width on entering it - a phenomenon he had demonstrated earlier on 3v.
On 8v he returns also to the eye - camera obscura analogy. To illustrate this he draws an object abcde. Such an object abcde recurs on D10v where the eye - camera obscura analogy is also at play. Such a logical arrangement of the notes may appear very convincing but it cannot be the order in which Leonardo wrote them. This comes to light from a detailed study of the text. On 2r, for instance, he describes the eyelid experiment which he subsequently carries out on 9v. n 2v he gives instructions to make a model of the eye which he carries out on 7v and 3v. On 7v he considers the possibility that the uvea might receive images. This he rejects on 10r in the lwoer part, where he confirms that they must go to the optic nerve, a theory which he demonstrates on 10v, 3v, 8r, 3r and 8v. What then might the order of composition have been?
We suggest that - as is the case with the Manuscript F - the order of folios today is as it was when Leonardo wrote the draft treatise. In which case it is very probable that he composed it in four stages: outer eye, inner eye, the beginning anew to study the pupil in detail, and finally ending with a series of notes on perception. Leonardo's reasoning may well have been as follows. He begins on 1r with a preliminary comment concerning visual and other powers. He wishes to add something on this topic and therefore leaves the rest of 1r blank. On 1v he gives a preliminary description of the eyelids and on 2r opposite, of the cornea.
In the margin of 2r he has an idea for a further experiment concerning eyelids. In order not to confuse his sequence, he turns to the last combination of a verso and recto page in the treatise, namely, 9v and 10r (cf. 1v and 2r). On 9v he develops his demonstration on eyelids and on 10r reformulates his claims concerning the arrangement of images on the surface of the cornea. This marks the end of stage one. The lower part of 10r remains blanks for the moment. He returns to the front part of the treatise, namely 2v, to begin stage two which is devoted to the inner eye. Here he outlines his demonstration that images are everywhere in the eye, sketches his theory of double inversion within the eye and mentions his plan to make a model of the visual process. In order to draft this idea he turns towards the back, to 7v, where he makes a preliminary model and explains his theory concerning the role of the uvea. This idea he reconsiders and then rejects in the remaining space on 10r. He turns the page and in the upper part of 10v, drafts a diagram of the complete visual process.
Not content with his model of the eye on 7v he draws a more elaborate version on 3v beneath which he outlines four alternative diagrams of the visual process. He explores further alternatives on 3r where he describes, but does not draw, an object K. This object (K) he draws on 8v where he integrates his interpretation of the visual process with his concepts of the visual field and central ray. On 8r he redraws this interpretation of the visual process, integrating features first discussed on 3v. This ends a second stage of his draft.
An unstated conclusion of these studies is that visual deceptions do not occur in the crystalline lens or other parts of the inner eye, but are produced by variations in pupil size and under certain conditions, by the eyelids. A third stage of the treatise is devoted specifically to pupils. It begins with further demonstrations concerning images being everywhere in the pupil (6v). On 6r he discusses pupils which are larger than life and mentions the astronomical context of these discussions. Comparative pupil studies follow on 5v and 5r. On 4v he writes another draft concerning images being everywehre in the pupil. On the upper part of 4r he writes a further note on pupil size.
In the fourth and final stage of his writing he adds a series of notes on perception on the unused parts of 4r, 8v, the whole of 9r, 7r and the bottom part of 10v, possibly in that order. The script of these passages appears to have been written by a different quill. On 7r, for instance, he writes two paragraphs using a fine quill and then finishes the page using a coarse one. It is significant that this reconstruction must also remain tentative. If even parts of individual pages were written at different times, it would be wrong to expect that this series of drafts could reveal a neat sequence of pages. Whether its structure is approached logically or chronologically, Manuscript D is not nearly as finished a treatise as it first appears.
3. Manuscript F
By contrast, the 21 page draft of an optical treatise within Manuscript F (see Chart 28) appears much less systematic than it actually is. Its focus is also different. Whereas D deals with the entire visual process, F concentrates on the role of eyelids, cornea and pupil with respect to astronomy. It sets out to show how the apparent size of stars is affected by illusions originating in the eye. On F 94v Leonardo begins with the intent to show how rays at the eye increase the apparent size of distant luminous bodies.7 This idea he reformulates as a question on F 95r, asking why the apparent size of a candle is not diminished when removed to a greater distance. His answer is interrupted by an apology:
This cannot be explained for lack of paper. But go back to the beginning of the book on page 40 which has the definition.
On F 40r (fig. 1496) he develops the diagram he had drafted on 95r (fig. 1494) and shows that although more distant objects subtend a smaller angle at the surface of the eye, refraction within the cornea has the effect that their apparent size is reduced in power but not in quantity (F39v). This claim is dramatic because it disposes of Euclid's theorem (see above pp. ) that the apparent size of objects depends strictly on the angle subtended at the eye.
Chart 28. Sequence of folios of the draft treatise on optics within Manuscript F.
Leonardo goes on to claim that changes in intensity govern changes in pupil size, namely, that the pupil increases to the extent that light decreases. This answers his question, posed on 94v, 95r and 40v, why objects do not appear smaller at a distance. At the bottom of F39v he writes: "turn to page 37." On 37r, he refor;mulates his claims in terms of two propositions: first, that a smaller pupil sees objects as smaller and less brightly, and second, that smaller objects send a lesser angle to the eye and conversely. This second proposition has a conventional Euclidean ring. But Leonardo goes on to cite the case of a bar of iron part of which is larger or smaller as a result of light intensity.
He is eager to consider all factors which affect light intensity and, in turn, alter the size of the pupil and apparent size and therefore pursues his idea (cf. Manuscript D 1v, 9v) and that eyelids can function as mirrors which reflect and magnify light coming to the eye and thereby affect estimates of apparent size. On F36v he uses apertures of various size to explore the connection between pupil size and apparent size. On F36r he summarizes his rules concerning light intensity and apparent size: that a more luminous object appears larger and conversely.
Below this he draws two objects clearly intended to represent stars (fig. 1500, cf. figs. 1495, 1501). Alongside, he explains that two luminous bodies positioned close to one another will appear united when seen from afar. On F35v he redraws these two light sources as two candles and pursues the theme, citing contemporary explanation which he rejects. His own explanation is that more distant objects have less intensity as a result of which the pupils expand and these objects appear larger. Meanwhile, on F36r, he had noted that if images converged to a mathematical point in the eye, it would not be possible to distinguish them separately. He restates this problem on F34r, adding that since we see images as being separate from one another, it follows that they do not end in a point.
On F33v there is an excursus to describe devices to test "how rays penetrate liquid bodies." On F33r, using a small aperture, he describes an experiment to show that pupil size and apparent size are intimately linked and, on F32v, adapts this to show that the image of a star passing through an aperture is everywhere in the eye and not reduced to a point. Further demonstrations on this theme follow on F32v, 32r and 28r. On F31v he discusses the arrangement of images of stars on the surface of the eye and mentions the problem of occlusion. On F31r he considers the occlusion of a dark object on a bright background. The non-occlusion of small objects provides him with a further demonstration that images are "all in all the eye" (F31r-30v).
On F37r he had mentioned the role of eyelids in convex mirrors. This he examines in greater detail on F30r, 29v and 29r. On F28v he raises further problems of optics and perception: why a hemispherical bubble produces a cross-shaped image in water and why objects smaller than the eye are not seen. On 28r he drafts another version of his demonstration that visual power is spread throughout the eye. Here the draft treatise on optics ends. As has been shown, it deals primarily with the eyelids, cornea and pupil, illusions arising therin and related perceptual problems. This stands in contrast to Manuscript D which deals with the entire visual process.
Chart 29. Correspondences of topics and problems in Mss. D and F.
Even so, the common features of Manuscripts D and F should not be overlooked. In both, Leonardo is concerned with sources of illusion in the eye. In both, he devotes more attention to the pupil than to any other part of the eye (see Chart 29). In Manuscript D he explores the idea that pupil size determines apparent size. In Manuscript F he develops this idea with respect to light sources. When a light source is close to the eye the pupil contracts and hence the light source appears amall. As the light source moves further back its intensity is less. This causes the pupil to expand and hence the more distant object does not appear smaller and may even appear larger. In the Manuscript F Leonardo shows that this light source could be a candle. But it could equally be a star. An astronomical context pervades the entire draft. This is no coincidence. In the chapters that follow it will be shown that Manuscripts D and F were intended to serve as chapters in a larger treatise on astronomy.
Reconstruction of Manuscript D (40 pages)
Last Update: July 10, 1999