spectator. This is termed violent or sudden perspective, to avoid which a point of distance is chosen that will look agreeable. The breadth of the squares being determined by the diagonal line running to the point of distance where it cuts through the lines of the pavement, which run to the point of sight, the farther this point is removed the more level the ground will appear, as represented in Fig. 12.

Point of sight.

Fig. 12.

B Point of distance.

ANGLES.

What we have hitherto said more immediately applies to parallel perspective, so named from all the lines which intersect those running to the point of sight, being parallel with the base line. When, however, a square, or any cubical form, is viewed at the angle, the two sides will not appear to vanish in the point of sight, but run to two points on the horizontal line, called vanishing points; and this mode of treating the subject is called angular perspective. Now, these two points are always at an equal distance from each other, which is one-fourth of a circle. Therefore, if one is determined upon, the other is easily found; for, as one departs from the point of sight, the other appears to approach it, as any one may perceive by turning around a sheet of paper, or a book, from a situation where one side is parallel with the base line, until it is viewed upon the angle. The cause, of this, perhaps, may be more clearly explained by the following figure:

B

Fig. 13.

D

Suppose the circle to represent the line of the horizon, which is the true representation of it when viewed out at sea, or where no obstruction intercepts it, for then the water, coming in contact with the sky, presents a circular horizontal line. If a person, therefore, was placed at D, and, looking to the point a, the line c would be parallel with the base, being at right angles with A, and, consequently, occupying one-fourth of a circle; but, if he turned in the direction of в, then a and c would become vanishing points, though still at equal distances upon the horizontal line, and would appear thus:

Fig. 14.

In a panorama, which is a circular canvas, viewed from the center, this mode of measuring the various points is found to agree perfectly with the natural representation of objects.

CIRCLES.

If any one takes a drinking glass or cup in his hand, with the mouth of it toward him, and gradually turns it from him, carefully watching it passing through all the elliptical forms, until the brim becomes a straight line in appearance, he will have a correct idea how it is that columns, or other circular objects, assume an oval shape at the top or bottom, according as they are below or above the eye. Or, if he holds the cup with the side downward, and turns the mouth gradually around toward him, he will perceive the cause why arches, or circular gateways, appear elliptical in a side view. It arises from parts of the circle being more foreshortened than other parts; that is to say, those parts which come more in the line of the visual rays. For example, let a circle be divided into equal parts, and suppose the eye of the spectator placed at A, those parts which lie in the direction of the rays of vision, B, occupy less space on the line c, which cuts through them, and, when drawn upon a flat surface, would present an appearance like D, Fig. 16. Or imagine a line drawn through the center, parallel with the base line, and which accordingly retains its exact length. Those portions of the circular line which lie in the same direction are less diminished, while the other parts, lying in an opposite direction, naturally become subject to the greatest degree of foreshortening, as in Fig. 17.

Having now gone through the several forms of a triangle, square and circle, I shall here recapitulate the influence of perspective upon their

several lines. We have seen that lines are shortened according as they fall in the direction of the visual rays, and retain their original length only when they cut them at right angles. Now, this takes place wherever the objects are placed, whether near the foreground or in the distance, the eye of the spectator being a point from which imaginary lines radiate in any direction, and which are termed rays of vision, and along which imaginary lines all objects are received upon the retina; and, though in

painting we are obliged to delineate everything upon a flat surface, yet, properly speaking, the line which cuts through these rays at equal distance from the eye is circular. We have seen also that all objects diminish in size according to their distance from the spectator, and that this diminution is more or less sudden according to the closeness of the spectator to the object. Upon this matter the taste and judgment of the artist is shown, because, though true according to Nature, yet it may be repre

Fig. 17.

Kepler, who in 1600 was the discoverer of the seat of vision on the retina, says as to the images of objects being inverted in the eye, it is the business of the mind to trace the progress of them through the pupil, and refer them to those places of the objects themselves from which they seem to have proceeded.

sented with a very bad effect, and one figure of a group, or one column of a row, may be rendered preposterously large, so as to offend the eye, which, though at all times pleased with the truth, yet will be more delighted when that truth is rendered agreeable. When this distortion takes place in reality, we naturally change our position, until the eye is satisfied; but in painting, the whole being a flat surface, we change our position in vain.

We have also seen that all horizontal surfaces of objects diminish in breadth as they approach the horizontal line, and regain their true width when they depart from it, either by being immediately above the eye or directly under it, as may be perceived by the following diagram:

A

Fig. 18.

Horizontal line.

Now, this rule applies to all flat surfaces, whether approaching the horizontal line, in consequence of their distance from the spectator, or from being placed at different degrees of height; for, if they reach the eye in the direction of an angle of 45 degrees, which is equidistant between a perpendicular and a horizontal line, they will be diminished in apparent width exactly one-half. If they are viewed at a greater or smaller angle, they will increase or diminish in the same degree. This is also the cause why surfaces of objects whose lines are at right angles with their base

7

Reynolds, in a note upon Fresnoy's Art of Painting, says, "The rules of perspective, as well as all other rules, may be injudiciously applied, and it must be acknowledged that a misapplication of them is but too frequently found even in the works of the most considerable artists. It is not uncommon to see a figure on the foreground represented near twice the size of another which is supposed to be removed but a few feet behind it; this, though true according to rule, will appear monstrous. This error proceeds from placing the point of distance too near the point of sight, by which means the diminution of objects is so sudden as to appear unnatural, unless you stand so near the picture as the point of distance requires, which would be too near for the eye to comprehend the whole picture; whereas if the point of distance is removed so far as the spectator may be supposed to stand in order to see commodiously, and take within his view the whole, the figures behind would then suffer under no such violent diminution."

line increase in length as they depart from the point of sight, either to the left hand or to the right, as may be seen by turning the diagram around, and making the line on which the eye of the spectator is placed a horizontal line in place of a perpendicular. This may appear too much a repetition of what has already been said respecting the cause of objects becoming foreshortened; but, as it is the base on which all rules for true drawing are founded, it must be viewed in every position, that the student may thoroughly comprehend it.

When the mind of the student is informed of the various causes operating upon lines so as to change their appearance to the eye, let him look abroad upon natural objects, and contemplate the various changes produced in their forms by their situation, so that his eye may become familiar with those alterations in form, and his mind enriched by a variety of examples; thus making Nature furnish him with a thousand diagrams, which he ought to draw and write down his remarks upon. He will, by this method, not only educate his eye, but improve his mind at the same time, the study of drawing being intimately connected with observation and reflection.

Having now endeavored to explain the leading principles of perspective, I shall proceed to put them into practical application; but I must premise that it is an essential requisite, before proceeding to delineate any object, that we make ourselves thoroughly acquainted with its general character, otherwise the eye cannot convey to us its image distinctly; neither can the hand render it with energy or precision. Let us take, for example, the human face, the component parts of which every one is acquainted with; yet the niceties of distinction in the several features few eyes can perceive, or render with perfect accuracy. This oftcner arises from a want of due examination, so as to be able to guide the eye, than from any deficiency in the eye itself; hence we perceive, in the drawings of children and rude nations, a profile with the eye represented as if viewed in front, or a full view of the face with the nose as if seen in profile. To avoid such incongruities, therefore, the eye must be taught to see the changes which take place, and the mind be made acquainted with the causes of such change. In illustration of which, if we take a plaster cast or mask of the face, such as is represented in Fig. 19, and draw a line down the center, from the forehead to the chin, we perceive, when viewed directly

8

Mengs, speaking of design, which he defines as comprehending the outline, or the circumference of things, including the proportion of their length, breadth and form, says, "This part is composed of two principal divisions, the knowledge of the proper form of a thing, and the manner of seeing it; the one depending upon geometry, the other upon optics: the first implies a knowledge of their optical appearance from the view presented to the sight; this pictorial geometry is necessary to enable the student to delineate with correctness and feeling, and which can only be acquired by careful habit of seeing and drawing with attention. This is the fundamental basis of design, without which it will be impossible to render theoretic knowledge available: for, as in painting, we must express the forms which we see in Nature as they present themselves to our sight, and as their beauty depends upon that little, more or less; which decides their character, so a knowledge of that variation enables us to give a true representation."