are indistinct in the shadows and in the high lights; but in the portions between the light and the shadows they are highly conspicuous. 156. OF PAINTING. Among objects in various degrees of shade, when the light proceeds from a single source, there will be the same proportion in their shadows as in the natural diminution of the light and the same must be understood of the degrees of light. 157. A single and distinct luminous body causes stronger relief in the object than a diffused light; as may be seen by comparing one side of a landscape illuminated by the sun, and one overshadowed by clouds, and so illuminated only by the diffused light of the atmosphere. THIRD BOOK ON LIGHT AND SHADE. Definition of derived shadow (158. 159). 158. Derived shadow cannot exist without primary shadow. This is proved by the first of this which says: Darkness is the total absence of light, and shadow is an alleviation of darkness and of light, and it is more or less dark or light in proportion as the darkness is modified by the light. 159. Shadow is diminution of light. Darkness is absence of light. Shadow is divided into two kinds, of which the first is called primary shadow, the second is derived shadow. The primary shadow is always the basis of the derived shadow. The edges of the derived shadow are straight lines. 39 [Footnote: The theory of the ombra dirivativa_--a technical expression for which there is no precise English equivalent is elaborate- ly treated by Leonardo. But both text and diagrams (as Pl. IV, 1-3 and Pl. V) must at once convince the student that the distinction he makes between ombra primitiva and ombra dirivativa is not merely justifiable but scientific. Ombra dirivativa is by no means a mere abstract idea. This is easily proved by repeating the experiment made by Leonardo, and by filling with smoke the room in which the existence of the ombra dirivativa is investigated, when the shadow becomes visible. Nor is it difficult to perceive how much of Leonardo's teaching depended on this theory. The recognised, but extremely complicated science of cast shadows--percussione dell' ombre dirivative as Leonardo calls them--is thus rendered more intelligible if not actually simpler, and we must assume this theory as our chief guide through the investigations which follow.] The darkness of the derived shadow diminishes in proportion as it is remote from the primary shadow. Different sorts of derived shadows (160-162). 160. SHADOW AND LIGHT. The forms of shadows are three: inasmuch as if the solid body which casts the shadow is equal (in size) to the light, the shadow resembles a column without any termination (in length). If the body is larger than the light the shadow resembles a truncated and inverted pyramid, and its length has also no defined termination. But if the body is smaller than the light, the shadow will resemble a pyramid and come to an end, as is seen in eclipses of the moon. 161. OF SIMPLE DERIVED SHADOWS. The simple derived shadow is of two kinds: one kind which has its length defined, and two kinds which are undefined; and the defined shadow is pyramidal. Of the two undefined, one is a column and the other spreads out; and all three have rectilinear outlines. But the converging, that is the pyramidal, shadow proceeds from a body that is smaller than the light, and the columnar from a body equal in size to the light, and the spreading shadow from a body larger than the light; &c. OF COMPOUND DERIVED SHADOWS. Compound derived shadows are of two kinds; that is columnar and spreading. 162. OF SHADOW. Derived shadows are of three kinds of which one is spreading, the second columnar, the third converging to the point where the two sides meet and intersect, and beyond this intersection the sides are infinitely prolonged or straight lines. And if you say, this shadow must terminate at the angle where the sides meet and extend no farther, I deny this, because above in the first on shadow I have proved: that a thing is completely terminated when no portion of it goes beyond its terminating lines. Now here, in this shadow, we see the converse of this, in as much as where this derived shadow originates we obviously have the figures of two pyramids of shad-ow which meet at their angles. Hence, if, as [my] opponent says, the first pyramid of shadow terminates the derivative shadow at the angle whence it starts, then the second pyramid of shadow--so says the adversary--must be caused by the angle and not from the body in shadow; and this is disproved with the help of the 2nd of this which says: Shadow is a condition produced by a body casting a shadow, and interposed between this shadow and the luminous body. By this it is made clear that the shadow is not produced by the angle of the derived shadow but only by the body casting the shadow; &c. If a spherical solid body is illuminated by a light of elongated form the shadow produced by the longest portion of this light will have less defined outlines than that which is produced by the breadth of the same light. And this is proved by what was said before, which is: That a shadow will have less defined outlines in proportion as the light which causes it is larger, and conversely, the outlines are clearer in proportion as it is smaller. [Footnote: The two diagrams to this chapter are on Plate IV, No. 1.] On the relation of derived and primary shadow (163-165). 40 163. The derived shadow can never resemble the body from which it proceeds unless the light is of the same form and size as the body causing the shadow. The derived shadow cannot be of the same form as the primary shadow unless it is intercepted by a plane parallel to it. 164. HOW A CAST SHADOW CAN NEVER BE OF THE SAME SIZE AS THE BODY THAT CASTS IT. If the rays of light proceed, as experience shows, from a single point and are diffused in a sphere round this point, radiating and dispersed through the air, the farther they spread the wider they must spread; and an object placed between the light and a wall is always imaged larger in its shadow, because the rays that strike it [Footnote: 7. The following lines are wanting to complete the logical connection.] would, by the time they have reached the wall, have become larger. 165. Any shadow cast by a body in light and shade is of the same nature and character as that which is inseparable from the body. The centre of the length of a shadow always corresponds to that of the luminous body [Footnote 6: This second statement of the same idea as in the former sentence, but in different words, does not, in the original, come next to the foregoing; sections 172 and 127 are placed between them.]. It is inevitable that every shadow must have its centre in a line with the centre of the light. On the shape of derived shadows (166-174). 166. OF THE PYRAMIDAL SHADOW. The pyramidal shadow produced by a columnar body will be narrower than the body itself in proportion as the simple derived shadow is intersected farther from the body which casts it. [Footnote 166: Compare the first diagram to No. 161. If we here conceive of the outlines of the pyramid of shadow on the ground as prolonged beyond its apex this gives rise to a second pyramid; this is what is spoken of at the beginning of No. 166.] 167. The cast shadow will be longest when the light is lowest. The cast shadow will be shortest when the light is highest. 168. Both the primary and derived shadow will be larger when caused by the light of a candle than by diffused light. The difference between the larger and smaller shadows will be in inverse proportion to the larger and smaller lights causing them. [Footnote: In the diagrams A stands for celo (sky), B for cadela (candle).] 169. ALL BODIES, IN PROPORTION AS THEY ARE NEARER TO, OR FARTHER FROM THE SOURCE OF LIGHT, WILL PRODUCE LONGER OR SHORTER DERIVED SHADOWS. Among bodies of equal size, that one which is illuminated by the largest light will have the shortest shadow. Experiment confirms this proposition. Thus the body m n is surrounded by a larger amount of light than the body p q, as is shown above. Let us say that v c a b d x is the sky, the source of light, and that s t is a window by which the luminous rays enter, and so m n and p q are bod- ies in light and shade as exposed to this light; m n will have a small derived shadow, because its original shadow will be small; and the derivative light will be large, again, because the original light c d will be large and p q will have more derived shadow because its 41 original shadow will be larger, and its derived light will be smaller than that of the body m n because that portion of the hemisphere a b which illuminates it is smaller than the hemisphere c d which illuminates the body m n. [Footnote: The diagram, given on Pl. IV, No. 2, stands in the original between lines 2 and 7, while the text of lines 3 to 6 is written on its left side. In the reproduction of this diagram the letter v at the outer right-hand end has been omitted.] 170. The shadow m bears the same proportion to the shadow n as the line b c to the line f c. 171. OF PAINTING. Of different shadows of equal strength that which is nearest the eye will seem the least strong. Why is the shadow e a b in the first grade of strength, b c in the second; c d in the third? The reason is that as from e a b the sky is nowhere visible, it gets no light whatever from the sky, and so has no direct [primary] light. b c faces the portion of the sky f g and is illuminated by it. c d faces the sky at h k. c d, being exposed to a larger extent of sky than b c, it is reasonable that it should be more lighted. And thus, up to a certain distance, the wall a d will grow lighter for the reasons here given, until the darkness of the room overpowers the light from the window. 172. When the light of the atmosphere is restricted [by an opening] and illuminates bodies which cast shadows, these bodies being
