The Notebooks

FIRST BOOK ON LIGHT AND SHADE. On the nature of light (130. 131). 130. The reason by which we know that a light radiates from a single centre is this: We plainly see that a large light is often much broader than some small object which nevertheless--and although the rays [of the large light] are much more than twice the extent [of the small body]--always has its shadow cast on the nearest surface very visibly. Let _c f_ be a broad light and _n_ be the object in front of it, casting a shadow on the plane, and let _a b_ be the plane. It is clear that it is not the broad light that will cast the shadow _n_ on the plane, but that the light has within it a centre is shown by this experiment. The shadow falls on the plane as is shown at _m o t r_. [Footnote 13: In the original MS. no explanatory text is placed after this title-line; but a space is left for it and the text beginning at line 15 comes next.] Why, to two [eyes] or in front of two eyes do 3 objects appear as two? Why, when you estimate the direction of an object with two sights the nearer appears confused. I say that the eye projects an infinite number of lines which mingle or join those reaching it which come to it from the object looked at. And it is only the central and sensible line that can discern and discriminate colours and objects; all the others are false and illusory. And if you place 2 objects at half an arm's length apart if the nearer of the two is close to the eye its form will remain far more confused than that of the second; the reason is that the first is overcome by a greater number of false lines than the second and so is rendered vague. Light acts in the same manner, for in the effects of its lines (=rays), and particularly in perspective, it much resembles the eye; and its central rays are what cast the true shadow. When the object in front of it is too quickly overcome with dim rays it will cast a broad and disproportionate shadow, ill defined; but when the object which is to cast the shadow and cuts off the rays near to the place where the shadow falls, then the shadow is distinct; and the more so in proportion as the light is far off, because at a long distance the central ray is less overcome by false rays; because the lines from the eye and the solar and other luminous rays passing through the atmosphere are obliged to travel in straight lines. Unless they are deflected by a denser or rarer air, when they will be bent at some point, but so long as the air is free from grossness or moisture they will preserve their direct course, always carrying the image of the object that intercepts them back to their point of origin. And if this is the eye, the intercepting object will be seen by its colour, as well as by form and size. But if the intercepting plane has in it some small perforation opening into a darker chamber--not darker in colour, but by absence of light--you will see the rays enter through this hole and transmitting to the plane beyond all the details of the object they proceed from both as to colour and form; only every thing will be upside down. But the size [of the image] where the lines are reconstructed will be in proportion to the relative distance of the aperture from the plane on which the lines fall [on one hand] and from their origin [on the other]. There they intersect and form 2 pyramids with their point meeting [a common apex] and their bases opposite. Let _a b_ be the point of origin of the lines, _d e_ the first plane, and _c_ the aperture with the intersection of the lines; _f g_ is the inner plane. You will find that _a_ falls upon the inner plane below at _g_, and _b_ which is below will go up to the spot _f_; it will be quite evident to experimenters that every luminous body has in itself a core or centre, from which and to which all the lines radiate which are sent forth by the surface of the luminous body and reflected back to it; or which, having been thrown out and not intercepted, are dispersed in the air. 131. THE RAYS WHETHER SHADED OR LUMINOUS HAVE GREATER STRENGTH AND EFFECT AT THEIR POINTS THAN AT THEIR SIDES. Although the points of luminous pyramids may extend into shaded places and those of pyramids of shadow into illuminated places, and though among the luminous pyramids one may start from a broader base than another; nevertheless, if by reason of their various length these luminous pyramids acquire angles of equal size their light will be equal; and the case will be the same with the pyramids of shadow; as may be seen in the intersected pyramids _a b c_ and _d e f_, which though their bases differ in size are equal as to breadth and light. [Footnote: 51--55: This supplementary paragraph is indicated as being a continuation of line 45, by two small crosses.] The difference between light and lustre (132--135). 132. Of the difference between light and lustre; and that lustre is not included among colours, but is saturation of whiteness, and derived from the surface of wet bodies; light partakes of the colour of the object which reflects it (to the eye) as gold or silver or the like. 133. OF THE HIGHEST LIGHTS WHICH TURN AND MOVE AS THE EYE MOVES WHICH SEES THE OBJECT. Suppose the body to be the round object figured here and let the light be at the point _a_, and let the illuminated side of the object be _b c_ and the eye at the point _d_: I say that, as lustre is every where and complete in each part, if you stand at the point _d_ the lustre will appear at _c_, and in proportion as the eye moves from _d_ to _a_, the lustre will move from _c_ to _n_. 134. OF PAINTING. Heigh light or lustre on any object is not situated [necessarily] in the middle of an illuminated object, but moves as and where the eye moves in looking at it. 135. OF LIGHT AND LUSTRE. What is the difference between light and the lustre which is seen on the polished surface of opaque bodies? The lights which are produced from the polished surface of opaque bodies will be stationary on stationary objects even if the eye on which they strike moves. But reflected lights will, on those same objects, appear in as many different places on the surface as different positions are taken by the eye. WHAT BODIES HAVE LIGHT UPON THEM WITHOUT LUSTRE? Opaque bodies which have a hard and rough surface never display any lustre in any portion of the side on which the light falls. WHAT BODIES WILL DISPLAY LUSTRE BUT NOT LOOK ILLUMINATED? Those bodies which are opaque and hard with a hard surface reflect light [lustre] from every spot on the illuminated side which is in a position to receive light at the same angle of incidence as they occupy with regard to the eye; but, as the surface mirrors all the surrounding objects, the illuminated [body] is not recognisable in these portions of the illuminated body. 136. The relations of luminous to illuminated bodies. The middle of the light and shade on an object in light and shade is opposite to the middle of the primary light. All light and shadow expresses itself in pyramidal lines. The middle of the shadow on any object must necessarily be opposite the middle of its light, with a direct line passing through the centre of the body. The middle of the light will be at _a_, that of the shadow at _b_. [Again, in bodies shown in light and shade the middle of each must coincide with the centre of the body, and a straight line will pass through both and through that centre.] [Footnote: In the original MS., at the spot marked _a_ of the first diagram Leonardo wrote _primitiuo_, and at the spot marked _c_--_primitiva_ (primary); at the spot marked _b_ he wrote _dirivatiuo_ and at _d deriuatiua_ (derived).] Experiments on the relation of light and shadow within a room (137--140). 137. SHOWS HOW LIGHT FROM ANY SIDE CONVERGES TO ONE POINT. Although the balls _a b c_ are lighted from one window, nevertheless, if you follow the lines of their shadows you will see they intersect at a point forming the angle _n_. [Footnote: The diagram belonging to this passage is slightly sketched on Pl. XXXII; a square with three balls below it. The first three lines of the text belonging to it are written above the sketch and the six others below it.] 138. Every shadow cast by a body has a central line directed to a single point produced by the intersection of luminous lines in the middle of the opening and thickness of the window. The proposition stated above, is plainly seen by experiment. Thus if you draw a place with a window looking northwards, and let this be _s f_, you will see a line starting from the horizon to the east, which, touching the 2 angles of the window _o f_, reaches _d_; and from the horizon on the west another line, touching the other 2 angles _r s_, and ending at _c_; and their intersection falls exactly in the middle of the opening and thickness of the window. Again, you can still better confirm this proof by placing two sticks, as shown at _g h_; and you will see the line drawn from the centre of the shadow directed to the centre _m_ and prolonged to the horizon _n f_. [Footnote: _B_ here stands for _cerchio del' orizonte tramontano_ on the original diagram (the circle of the horizon towards the North); _A_ for _levante_ (East) and _C_ for _ponete_ (West).]