PERSPECTIVE. There are two kinds of perspective delineation with which the photographer is concerned, viz., " Plane," and " Panoramic Perspective.' In plane perspective, objects are represented upon a vertical plane placed between them and the spectator. Straight lines, called " visual rays," are supposed to be drawn from the various angular points A, B, C, 8r,c., of the objects, to the eye, and where these lines perforate the vertical plane, or " plane of the picture," as it is called, are corresponding points a, b, c, &c., through which, if the figure be completed, it is the plane perspective representation of the objects as seen from the point occupied by the eye (not eyes) of the spectator. According to this definition a plane perspective view is nothing more than a plane section of the system of pyramids of which the visual rays are the edges and the eye the common vertex ; the eye being considered a mathematical point. The rules of perspective, therefore, merely relate to the cutting of pyramids by a plane, and are purely geometrical, not referring in any way to the structure of the eye, or the image formed upon the retina, or the rules of optics. Perspective is nothing more than a very simple problem in solid geometry, and it is marvellous to find that so little is accurately knovni of it by artists, and that so many elaborate and expensive works should have been written about it, when in fact the whole thing lies in a nut-shell, as we shall now show ; not however without calling on the reader for his patient attention, and careful study of our remarks.
Let us first suppose the object to be represented to be an infinite straight line, making an angle, 0, with the plane of the picture, and meeting it in the point A. Then, in order to draw the perspective view of this line upon the plane of the picture, it is evident that we should require to join the point A with some other point X. The question becomes how to find this point X. If it were possible to draw a visual ray from the eye to the end of an infinite straight line, the point where that visual ray would cut the plane of the picture would be the point X required. But is it possible to draw such a
line ? It is. We have simply to draw through the eye a line parallel to the given infinite straight line, and the point X where this line cuts the plane of the picture is found at once ; for although parallel straight lines do not meet at any finite distance, they may be considered as meetina at an infinite distance, infinite being only another term for " not finite," and the second form of the expression being identical with the first. But this is becoming metaphysical. Practically, the problem is solved. The finite line AX is the per spective view of the infinite line proceecling from A, and making an angle with the plane of the picture.
Next, suppose any number of other infinite straight lines to make the same angle co with the plane of the picture, and to meet it in points B, C, D, Sic. It is evident that the perspective views of all these straight lines would be terminated in a common point X, and would consist of lines A X, B X, C X, &c. radiating from X ; this point is therefore called the " vanishing point" of that ptuticular system of parallel straight lines.
Hence we arrive at the following general rule:— The vanishing point of any system of parallel straight lines is the point where a line drawn through. the eye parallel to that system cuts the plane of the picture.
If a horizontal plane be drawn through the eye the line in which it interseas the plane of the picture is called the " horizontal line ;" and if a hne be drawn from the eye perpendicular to the horizontal line, the point in which it cuts it is called the " point of sight." Hence it follows that lst. The vanishing point of a system of parallel horizontal lines is upon the " horizontal line " of the picture; the point being found by drawing through the eye a line parallel to any one of the system of lines.