with every new plane MN; or if the object is cur vilinear, tangents will always pass through the lines CA' and DB respectively, except when they are perpendicular.

Example 4. Let a lamp O, fig. 15, plate 31, throw a shadow on the body RSUT, and let QTt be the central line of the shadow from the parallelogram, AB, upon the ground; draw OP, Gu, parallel to QT, and from T to OP draw t P, touching the plane US of the body; from P draw PS u, Pw U, cutting the extremities of the shadow in Ú and u, and w UuS will be the shadow of A B upon the face US; proceed in like manner with all the other illumined faces.

N. B. If t P never meets O P, it denotes the face of the body to be parallel to AB, and the shadow on that face to be a parallelogram.

The shadows, being thus ascertained, may be put into perspective by the foregoing rules.

PROBLEM 10. To find the reflections of objects upon polished surfaces.

Let fall a perpendicular upon the reflecting plane, to which draw a radial from the eye, as much below the horizontal line, as the real object appears to be

above it.

Example 1. Let AB, fig. 18, plate 31, be any object placed on the water; from B draw B b, perpendicular to the surface Ab, which continue till the angles B E b and C E b are equal; that is, (E b being a horizontal line) till b c is equal to b B, and b C will be the reflection of A B.

Example 2. When objects are upright, the lines may be produced below the horizontal line, as much as the real ones are above it.

OF PARALLEL, OR MILITARY PERSPECTIVE.

In this kind of projections, the eye is supposed to be placed at an indefinite distance from the ob

Ject in the diagonal, and looking down upon it in an angle of 45°, so that the top, one side, and one end, are seen under the same angle, and therefore appear in their true proportions with respect to each other; and therefore heights, lengths, and breadths must be laid down by the same scale, and all parallel lines made parallel, see fig. A, plate 30.

OF AERIAL PERSPECTIVE.

Before we can give rules for regulating the force of lights and shades in a picture, we must consider what degree of it the bodies themselves are endued with, according to their several positions with respect to the illuminating body.

Proposition 3. The intensity of light upon any plane is reciprocally as the square of the distance of that plane from the illuminating body.

Let ABCD, fig. 16, plate 31, be the shadow of the square a bed upon a plane parallel to it, which projection will therefore be a square, and in proportion to a bed as the square upon OA to that upon Oa; therefore since the real quantity of light is the same as would be received upon ABCD, the intensity of it is reciprocally as the square upon AB to the square upon a b, or as the square OA to the square Oa.

For example, if parallel planes are at the distance of one, two, and three feet from a luminous point, the intensity of light upon them would be one, onefourth, one-tenth, &c.

Corollary. All parallel planes are equally illuminated by the sun at the same moment.

For, his rays being parallel, the squares abcd, and ABCD are equal.

Proposition 4. If the sun's beams fall perpendicular upon one face AB, fig. 17, plate 31, of an object, and inclined upon another AC, the intensity of light on the faces, is as radius to the sine of the angle of incidence.

Produce A B to b, the quantity of light A b receives is the same as would be received on AC if b A were away; therefore the brightness is as AC to A b, that is, the brightness of AB, or Ab is to that of AC as AC to A b, or as radius to sine of the angle of incidence A C b.

Proposition 5. A plane uniformly enlightened does not appear so to an eye in different situations.

For, as all bodies are porous, the little exuberances will have their light and dark sides, and the eye will view more of the former, as it is more nearly situated in a line with the rays of light, and more of the latter, the more it faces them.

The subject of this proposition is one great cause of the graduation of light upon the faces of buildings and other planes, and not altogether owing to a greater teint of air, as the artists call it, on that part which is the farthest off.

Remark. It is very necessary to observe, that transparent and polished bodies are not included among those mentioned in this proposition, for they seem most illuminated in that part which makes the angle of reflection equal to that of incidence; but if bodies of this kind are not flat, as water when just broken by small rippling waves, then the light is reflected from some part of almost every wave, and so is extended to a great space, but is strongest perpendicular under the luminary, and gradually decreases on each side.

The case is the same in the sky which is brightest near the sun's apparent place, and graduates into a deeper azure as it retires farther off, and for a reason nearly the same; for the pellucid particles floating above us, having large interstices between them, act in the same manner as the rippling waves in disturbed water; and, therefore, the more obliquely the light strikes upon them, the more united their force will be to an eye situated in the proper angle of reflection.

Proposition 6. All shades and shadowing objects would be equally dark and indistinguishable, if they received no secondary or reflected light.

For, light is not visible itself, but by striking upon other bodies renders them so, and these enlightened bodies serve as lights to bodies otherwise in shade, and such lights are called secondary or reflected ones, the chief of which is the sky.

Proposition 7. Every body participates of the colour of the light by which it is illumined; for, blue rays thrown upon a yellow body will produce a green; red rays, purple; and purple rays, that is, blue and red, black.

Corollary. Hence shadows are often observed green in the morning or evening, for the sky is always very green at those times compared with other times of the day, owning to the warm rays being more copiously reflected downwards by the sun's beams striking more obliquely on the atmosphere, which partly acts as a prism, and the shadows become more blue, as the sky becomes so; but clouds are of all colours, and as they are denser than the blue part of the sky, they throw stronger reflections, and cause many accidental teints in the shadows of bodies; therefore, as the shadow of every body is partially enlightened by all the bodies surrounding it, it must partake of the colours of all of them; and this is the grand source of harmony in painting, of which system the colour of the original light serves as a key, and is to be attended as nicely to in painting as in

music.

Proposition 8. Bodies partake more of the colourof the sky, as they are farther off.

For, the sky being only a body of air every where surrounding us, its natural colour, supposed to be blue, the farther off any body is, the more of this blue air is intercepted between us and the body, and therefore the bluer it is, and that in proportion to its distance.`

OF INSTRUMENTS FOR DRAWING IN PERSPECTIVE.

Various have been the methods used to facilitate the practice of perspective, as well for those who understand, as those who are ignorant of that art; and, though some have supposed that the warmth of imagination and luxuriance of fancy, which impels the mind to the cultivation of the fine arts, is not to be confined to mechanical modes, yet upon inquiry they will find, that the most able and accomplished artists are often obliged to have recourse to some rules, and to use some mechanical contrivances to guide and correct their pencil. So great is the difficulty, and so tedious the operation of putting objects in true perspective, that they trust mostly to their eye and habit for success; how well they succeed, we may decide from the portraits drawn by the best artists, and the different judgments formed concerning them. Mr. Eckhardt has well observed, that there is no artist who will be hardy enough to say, that he can delineate by the eye the same object twice with exactness, and preserve a just and similar proportion of parts in each. In one of the figures, we shall find some of the parts larger than in the other-both cannot be right: yet, supposing them perfectly the same, neither may be conformable to nature. Add to this, many situations of an object occur, which no eye, however habituated, can represent with accuracy.

On this account, I have a long time endeavoured to complete an instrument that should give the outline of an object with accuracy. These Essays have now swelled so far beyond my intentions, that I must be as concise as possible. I must, however, acknowledge the valuable hints communicated by Mr. Heywood, and other ingenious men.

The methods most generally in use are. 1. The camera obscura. 2. The glass medium or plane.