2nd. The vanishing point of a system of parallel horizontal lines at right angles to the plane of the picture is the "point of sight." Now we come to the case of the vanishing point of a system of parallel lines which are parallel to the plane of the picture ; that is, to the case in which the angle vanishes. These lines have no vanishing point, because the line drawn through the eye parallel to them never meets the picture. They are consequently represented by parallel lines in the picture.
Observe the practical conclusions : 1st. All vertical straight lines in nature are represented by vertical straight lines in the picture. They do not vanish towards a point in the zenith, as is generally erroneously supposed. In fact, in strict accuracy, vertical lines would vanish downwards towards the centre of gravity of the earth.
2nd. The horizontal lines of a building which are parallel to the plane of the picture are horizontal lines in the picture.
Should the reasoning by which these conclusions are established be thought somewhat metaphysical, then we may return to the case of the section of a pyramid. Place a square board vertically behind the plane of the picture, and parallel to it. Then, since the section of a pyramid by a plane parallel to its base is a figure similar to the base, the perspective view of the square is also a square, that is, neither the vertical nor the horizontal lines have any vanishing point.
We have now discussed the whole theory and mystery of plane perspective. If the reader has carefully followed our reasoning he will not require to spend his money in treatises on perspective, (which are generally full of gross blunders,) but may trust to his own good sense to apply the rules which we have established.
The following remarks should be borne in mind : In views of marine scenery, the horizontal line is always higher than the sea line, because of the dip of the visible horizon ; and the sea-line is a curve convex to the horizontal line, and most nearly touching it in the point of sight.
The perspective view of a sphere is an ellipse in every case, except that in which the line joining the eye and the centre of the sphere is perpendicular to the plane of the picture, so that the centre of the sphere is on the point of sight. For let a visual ray travel round a sphere, it sweeps out a cone with a circular base, and the oblique section of such a cone is an ellipse.
If the plane of the picture be inclined to the vertical, vertical lines have a vanishing point either above or below the horizontal line.
The reflections of vertical objects in water are vertical, and have no vanishing point, because the image of a vertical line is in the vertical produced beneath the surface of the water, and not in a hori zontal line lying upon the surface of the water, as it appears to be. When the reflection of a vertical line is not represented as a continua tion of that line, but as making an angle with it, the perspective is incorrect, no matter in what part of the picture the vertical line may be, or how situated with respect to the point of sight. The reflec tion of an object which is out of the perpendicular is not necessarily in the same straight line with it, but in general makes an angle with with it.
The reflection of the sun or moon is always vertically under it, no matter where the point of sight may be. Also, the bar of light pro duced by the reflection of the sun or moon in rippling water is always vertical, and does not appear to approach the spectator, as it is in correctly represented to do in many pictures. It is always a good plan, therefore, to take the point of sight immediately beneath the sun or moon, when they occur in a picture.
Some of the above remarks may be received with surprise and in credulity by some readers, but a little consideration will shew that they are strictly correct.
Panoramic Perspective is when the picture is represented upon a vertical cylinder, of which the eye is in the centre. In this kind of perspective the rules are somewhat more complicated, and need not be stated in this work ; it will be sufficient to observe that, in a panoramic picture flattened out, straight lines vanish in curves, not in straight lines.
When the image is formed upon the focussing scre,en of a camera having a small pin-hole in front instead of a lens, it is in perfectly true perspective ; for if we consider the pin-hole as the vertex of the system of pyramids formed by lines drawn from it to the objects, and that these lines are produced through the hole so 3,s to form another system, equal and similar to the former, but inverted, it is evident that the section of this second systpm made by the focussing screen is equal and similar to a section made by a screen plac,ed symmetri cally with it on the opposite side of the pin-hole, and therefore equal and similar to a perspective view obtained in the ordinary way, but inverted.