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IT IS A FIXED law in perspective that all lines parallel each to each, vanish in the distance at the same point upon the horizon. Take, for instance, a long row of telegraph poles. The line of the earth in which they are set, and the line running along the tops of the poles are parallel to each other, and seem to vanish on the horizon at the same point.- Two or any number of tracks laid parallel, apparently vanish at one point upon the horizon.
The horizon is that line in the distance where all planes, not just lines, but planes parallel to the earth’s surface, are seen to vanish. The horizon is always opposite the eye. The plane of the earth appears to converge upward toward it, and all planes above the plane of the eye or visual axis converge downward toward it. These planes vanish because the angle at which the furthermost visible borders of the earth's plane enters the eye, is so sharp the eye can scarcely record what is there. Our sense of sight fails at the horizon or plane of the eye because there is no longer an angle; the axis of the eye and the horizon are opposite.
Any plane above the horizon eventually converges downward toward the earth’s plane, and to all appearances becomes part of the horizon. If we take a more elevated position, that which was the horizon when we were standing on the earth's level is very distinctly seen, and the earth’s surface beyond the first horizon is seen from the elevated point for some distance further. The greater the elevation, the greater the distance the second horizon is formed beyond the first. On the other hand, if we remain on the earth’s level, and a plane above us is extended as far as the horizon, it continues to appear above the level of the eye and above the horizon, until it has receded sufficiently far from us, to enter the eye just as directly as the horizon does. It then becomes obliterated so far as our sight is concerned.
The ship’s mast is an instance of this. The plane of the top of the mast, while parallel to the earth, does not disappear as quickly as the earth’s surface, but is found above the earth’s horizon line, as is exemplified by seeing the mast above the horizon. As the ship recedes, the plane of the mast eventually lowers until the top of the mast becomes level with the earth's horizon, and the ship is no longer seen. The plane has vanished, to all appearances, at the horizon of the earth’s plane. Had a solid row of ships masts, the same height as the one seen at the horizon, been placed after the first ship, the result would be the same; the farthest ones would appear smaller and smaller, until the angle became identical with the axis of the eye.
In the Cellular Cosmogony, the rising and setting of the sun are explained by perspective foreshortening. The convexity of the heavens is parallel at all points to the concavity of the earth’s surface. The convex surface of a small ball centrally located within a larger hollow ball, is parallel to the concave surface of the larger ball at every point. A yolk within an egg is nearly so. The visible sun has its orbit around the heavens. This orbit is then parallel to the concave surface of the earth. Suppose it is twelve at noon; the sun would be directly over us. Its movement as it receded from us would be upward around the convexity of the heavens, while its appearance is downward until it seems to drop below the horizon. It is all due to the principle of perspective just described—the vanishing of planes parallel to the earth’s plane, at the horizon, or beyond it, which to all appearances is the same.
When the lower edge of the sun at setting has touched the horizon, it is because the plane at the lowest point of the sun has reached the point in the distance that brings it in line with the earth’s horizon line, and causes it to become obscured. While the sun is sinking it is really getting further away, until the plane of the top of the sun has also come in line with the horizon, or fallen in line behind it.
In the morning, when the sun travels down toward us on the convex arc of the heavens, the appearance is reversed. The plane of the top point of the sun comes into view first; when the sun is apparently rising it is actually coming toward us, until the plane of the lower point has become apparent at the horizon, and it is all in view over the horizon. The plane of the bottom or the top of the sun increases and increases in height as the sun comes toward us, just as the lines at the top of the telegraph poles do, as they approach the observer. There are many other points to consider in the phenomena of sunrise and sunset, but the law of perspective foreshortening is the first and most important principle to grasp before going into further detail.
The Flaming Sword · Vol. 27, No. 3 · Mar 1913 · PDF p. 14