figure, this due proportion is easily preserved, because each part is measured and laid down from a determined scale: with respect to trees, houses, animals, and other similar natural objects, however, the same accuracy is not to be attained, neither if it were attainable would it be applicable; for all external objects assume very various appearances, and demand very various representations in drawing or painting, according to their position with respect to the observer, their distance, their colour, their magnitude, and many other circumstances which determine the precise manner in which they must be imitated. This precise mode of imitation, far from being vague and uncertain, is founded on principles inherent in the nature of things, susceptible of strict geometrical demonstration; and that branch of geometry by which we are enabled to ascertain such imitations is termed Perspective.

Perspective. It may appear strange, but it is certainly true, that with the exception of one figure alone, we never see any object constantly as it really is. The only figure which in every possible position or point of view will always present the same appearance to the eye, is a sphere or globe, for in every attitude its outline is constantly a circle; a plane circular surface on the contrary will appear to be perfectly round only when the eye is perpendicular to its centre, or in the direction of the axis of the circle; in every other position, a circle assumes the appearance of an ellipse, until the eye come to be in the plane of its surface, when the circumference appears as a straight line.

Abstracting from all other considerations, we always judge of the magnitude of objects according to that of the angles formed in the eye by lines proceeding from their extremities, and all objects subtending equal angles at the eye, must be considered and represented as of equal magnitudes, thus in Plate fig. 1. let E be the eye of an observer, and a b any object within view, if lines be drawn aE

and

and E from the extremities of that object to the eye, the angle aEb will represent the magnitude of the object as judged of by the observer. Suppose another object cd, of exactly the same elevation with ab, to be situated at double the distance of the latter object, Ec being double Ea, then the angle formed at the eye by lines from the extremities, or dEc will be the perspective measure of the magnitude of the object cd: but in the similar triangles dEc and cEa, the side Ea being one half of the side Ec, the perpendicular de will be but one half of the perpendicular cd, which was made equal to ab; consequently, ae will be only one half of ab, and the angle aEe must be only one half of the angle aEb; therefore any object as ab, if removed to a distance twice as great as that of its first position, will subtend an angle at the eye only one-half of that subtended at its first position. Again, the angle aEe being equal to and indeed the same with the angle cEd, the objects ae and cd will subtend equal angles, or appear to be of equal magnitudes; consequently, any given object at any distance will appear of the same magnitude with another of double its magnitude, situated at double the distance of the first object.

Hence, we discover that the several objects fg, hk, &c. although really of different magnitudes must appear to an observer at E to be all equal, because owing to their different distances, they all subtend equal angles at his eye.

Hence, also, we learn why lines strictly parallel never appear to be so; for let the two lines ab and cd, (fig. 2) represent the two parallel sides of a gallery, an avenue or the like, it is evident from the figure, that the angle cEa formed by lines from opposite points, in the end of the avenue nearest the observer at E, is much greater than the angle dEb, similarly formed by lines from opposite points, in the further end of the avenue, the nearest end appearing in breadth equal to ca, while the farthest appears only in breadth as em: the distance therefore between the sides of

the

avenue, appearing to be unequal, the sides must appear to be inclined towards each other, with a tendency to unite at some remote point of the prospect, contrary to the essential property of parallel lines, which although produced both ways ad infinitum, would never approach or recede the one from the other. It is true indeed that the distance between two parallel lines must always bear a determinate proportion to their length, however extended they may be, and consequently that the angle formed at the eye, by lines from the most remote extremity, must always have a calculable. magnitude: but although this be geometrically the fact, still our sight being unable beyond certain limits to per ceive this subtended angle, the parallel lines may for every useful or sensible purpose be considered and represented as mutually tending to unite at some distant point.

When one stands before a mirror in a room, he observes his own figure, and part of the walls, furniture, &c. of the apartment reflected in the glass, each object in proportion to its position, magnitude, and distance, from the mirror, although reversed and apparently in another chamber to If the obwhich the glass seems to present an entrance. server stand sufficiently near to the mirror, and without moving from his position, trace with a pencil or otherwise on the glass, the boundaries of the various objects he sees reflected in it, the assemblage of figures thus drawn will be a correct representation (although reversed) of the several objects within his view at that point of sight. Again, if one stand at a window looking at the prospect without through a pane of the glass, and stedfastly keeping his position, draw on the surface of the glass a correct tracing of the trees, buildings, mountains, animals, ships, &c. &c. visible from his station, he will obtain a true representation of the external scenery, delineated on the plane of the glass in the window: this representation obtained by looking through the pane will be, as its name indeed imports,

VOL. II.

imports, a genuine perspective draught of the prospect before

him.

By attending to these two examples, we may comprehend the nature and principles of perspective, which is in fact nothing more than the method of representing on a plane surface the appearances of objects in their due gradations of position, magnitude, and distance. This is pecuJiarly obvious with respect to objects reflected from a mirFor; for there each evidently appears removed behind the glass, precisely to the same distance with the original object before it; as the observer approaches or recedes from the mirror, so does the reflected object proportionally approach or recede behind the glass.

Explanation of terms in Perspective.

The picture, means the paper, canvas, tablet, or other substance on which the representation of any object is drawn.

The centre of the picture, is that point where a line from the spectator's eye cuts the picture (or its plane produced if necessary) at right angles.

The distance of the picture, is the distance between the eye and the centre of the picture, or it is the length of a perpendicular, drawn from the eye to the centre of the picture. It is to be remembered, that by the centre of the picture is not meant the centre of the paper or canvas: on the contrary, these two points very seldom coincide, for the spectator is generally supposed to be situated nearer to the one side than to the other of the representation to be made, or nearer to the bottom than to the top, and in some cases the perpendicular from the eye may fall without the bounds of the representation, and consequently coincide only with its plane produced.

The point of view, is the situation of the eye of the spectator, elevated a few feet above the ground.

The