The Notebooks

139. Every shadow with all its variations, which becomes larger as its distance from the object is greater, has its external lines intersecting in the middle, between the light and the object. This proposition is very evident and is confirmed by experience. For, if _a b_ is a window without any object interposed, the luminous atmosphere to the right hand at _a_ is seen to the left at _d_. And the atmosphere at the left illuminates on the right at _c_, and the lines intersect at the point _m_. [Footnote: _A_ here stands for _levante_ (East), _B_ for _ponente_ (West).] 140. Every body in light and shade is situated between 2 pyramids one dark and the other luminous, one is visible the other is not. But this only happens when the light enters by a window. Supposing _a b_ to be the window and _r_ the body in light and shade, the light to the right hand _z_ will pass the object to the left and go on to _p_; the light to the left at _k_ will pass to the right of the object at _i_ and go on to _m_ and the two lines will intersect at _c_ and form a pyramid. Then again _a_ _b_ falls on the shaded body at _i_ _g_ and forms a pyramid _f_ _i_ _g_. _f_ will be dark because the light _a_ _b_ can never fall there; _i_ _g_ _c_ will be illuminated because the light falls upon it. Light and shadow with regard to the position of the eye (141--145). 141. Every shaded body that is larger than the pupil and that interposes between the luminous body and the eye will be seen dark. When the eye is placed between the luminous body and the objects illuminated by it, these objects will be seen without any shadow. [Footnote: The diagram which in the original stands above line 1 is given on Plate II, No 2. Then, after a blank space of about eight lines, the diagram Plate II No 3 is placed in the original. There is no explanation of it beyond the one line written under it.] 142. Why the 2 lights one on each side of a body having two pyramidal sides of an obtuse apex leave it devoid of shadow. [Footnote: The sketch illustrating this is on Plate XLI No 1.] 143. A body in shadow situated between the light and the eye can never display its illuminated portion unless the eye can see the whole of the primary light. [Footnote: _A_ stands for _corpo_ (body), _B_ for _lume_ (light).] 144. The eye which looks (at a spot) half way between the shadow and the light which surrounds the body in shadow will see that the deepest shadows on that body will meet the eye at equal angles, that is at the same angle as that of sight. [Footnote: In both these diagrams _A_ stands for _lume_ (light) _B_ for _ombra_ (shadow).] 145. OF THE DIFFERENT LIGHT AND SHADE IN VARIOUS ASPECTS AND OF OBJECTS PLACED IN THEM. If the sun is in the East and you look towards the West you will see every thing in full light and totally without shadow because you see them from the same side as the sun: and if you look towards the South or North you will see all objects in light and shade, because you see both the side towards the sun and the side away from it; and if you look towards the coming of the sun all objects will show you their shaded side, because on that side the sun cannot fall upon them. The law of the incidence of light. 146. The edges of a window which are illuminated by 2 lights of equal degrees of brightness will not reflect light of equal brightness into the chamber within. If _b_ is a candle and _a c_ our hemisphere both will illuminate the edges of the window _m_ _n_, but light _b_ will only illuminate _f g_ and the hemisphere _a_ will light all of _d e_. 147. OF PAINTING. That part of a body which receives the luminous rays at equal angles will be in a higher light than any other part of it. And the part which the luminous rays strike between less equal angles will be less strongly illuminated. SECOND BOOK ON LIGHT AND SHADE. Gradations of strength in the shadows (148. 149). 148. THAT PORTION OF A BODY IN LIGHT AND SHADE WILL BE LEAST LUMINOUS WHICH IS SEEN UNDER THE LEAST AMOUNT OF LIGHT. That part of the object which is marked _m_ is in the highest light because it faces the window _a d_ by the line _a f_; _n_ is in the second grade because the light _b d_ strikes it by the line _b e_; _o_ is in the third grade, as the light falls on it from _c d_ by the line _c h_; _p_ is the lowest light but one as _c d_ falls on it by the line _d v_; _q_ is the deepest shadow for no light falls on it from any part of the window. In proportion as _c d_ goes into _a d_ so will _n r s_ be darker than _m_, and all the rest is space without shadow. [Footnote: The diagram belonging to this chapter is No. 1 on Plate III. The letters _a b e d_ and _r_ are not reproduced in facsimile of the original, but have been replaced by ordinary type in the margin. 5-12. The original text of these lines is reproduced within the diagram.--Compare No 275.] 149. The light which falls on a shaded body at the acutest angle receives the highest light, and the darkest portion is that which receives it at an obtuse angle and both the light and the shadow form pyramids. The angle _c_ receives the highest grade of light because it is directly in front of the window _a b_ and the whole horizon of the sky _m x_. The angle _a_ differs but little from _c_ because the angles which divide it are not so unequal as those below, and only that portion of the horizon is intercepted which lies between _y_ and _x_. Although it gains as much on the other side its line is nevertheless not very strong because one angle is smaller than its fellow. The angles _e i_ will have less light because they do not see much of the light _m s_ and the light _v x_ and their angles are very unequal. Yhe angle _k_ and the angle _f_ are each placed between very unequal angles and therefore have but little light, because at _k_ it has only the light _p t_, and at _f_ only _t q_; _o g_ is the lowest grade of light because this part has no light at all from the sky; and thence come the lines which will reconstruct a pyramid that is the counterpart of the pyramid _c_; and this pyramid _l_ is in the first grade of shadow; for this too is placed between equal angles directly opposite to each other on either side of a straight line which passes through the centre of the body and goes to the centre of the light. The several luminous images cast within the frame of the window at the points _a_ and _b_ make a light which surrounds the derived shadow cast by the solid body at the points 4 and 6. The shaded images increase from _o g_ and end at 7 and 8. [Footnote: The diagram belonging to this chapter is No. 2 on Plate III. In the original it is placed between lines 3 and 4, and in the reproduction these are shown in part. The semi circle above is marked _orizonte_ (horizon). The number 6 at the left hand side, outside the facsimile, is in the place of a figure which has become indistinct in the original.]