Extracted text
Editorial transcription, lightly normalized from the scan. Line-break hyphenation, spacing, capitalization, and unmistakable OCR errors have been repaired; the claims remain those of The Flaming Sword.
The Open Court of Inquiry.
THE EDITOR.
The Question of Foreshortening.
Editor Flaming Sword:— Why does not a ship as it passes out to sea, become smaller and smaller until it entirely disappears from sight as a whole, as does the rising balloon, instead of disappearing hull first, if the ship is sailing upon a concave surface?— G. F. H., Ft. Worth, Texas.
The above question is submitted by a student of Koreshan Universology for the purpose of obtaining information, and not as an argument against the idea of the concavity. We judge from the number of questions asked on this point, that the simple principles of foreshortening must, for some reason or other, be really hard to grasp by the modern mind. However, we always take pleasure in endeavoring to make all points of inquiry as clear as possible. If by mental application to the facts and principles involved in the subject one can really comprehend how a ship disappears at sea, it is a matter of congratulation—in view of the fact that the modern scientists either cannot or will not understand it.
A balloon disappears in the open sky because the space it occupies foreshortens equally from all sides in accordance with principles of simple perspective. If we could suppose a ship sailing in the air in the place of the balloon, the whole would be reduced to the vanishing-point; its parts would contract together from top to bottom and from side to side. It would do so because it is not related to the tangible surface of sea or land. This simple kind of perspective is fairly well understood by the scientist, draughtsman, and artist. But we have met scientists and graduates of universities who knew nothing of the principles of geolinear foreshortening—in fact, the idea is new to the world. To the mind that does not take geolinear foreshortening into account, the disappearance of objects on the surface of the water's concavity is an insoluble enigma.
If we launch a toy ship upon the water and allow it to float from shore, it will gradually diminish in apparent size and become reduced to the vanishing-point—hull, sail, and top-mast all together, because it is small enough to vanish from sight before it reaches the horizon. The distance at which it will disappear on the water is about the same as that at which it would vanish from sight if passing out into open sky. The mind is wont to conceive that the same results should obtain in the case of vessels sailing on great concave bodies of water. But the factor of geolinear foreshortening makes all the difference in the world between the phenomena of large objects beyond the horizon and the simple vanishing of small objects between the horizon and the observer.
The earth is flat enough from accessible points of observation to admit of a vanishing-line of its surface. There is a point or line in the distance beyond which no surface can be seen. Why? Because contraction of the lateral space accelerates in proportion to the distance; and the point is soon reached when a given space subtends so small an angle as to make no impression upon the retina of the eye. That is, the first mile subtends a large angle; the second mile a much smaller angle, and so on, until at the horizon the angle becomes infinitesimal.
If no surface can be seen beyond the horizon, it is because the space above the water at the horizon point equal to the altitude of the observer has been reduced to the vanishing-point, and because the geolinear extense has also reached its vanishing-line. Consider perspective and geolinear foreshortening together, and picture in the mind a vessel beyond the horizon, and ask, how much of it will be invisible? So much of it as is embraced in the vanished space. That portion of the vessel which is above the space vanished or contracted to an angle too small to make an impression, still remains in sight. The vanishing point of ten feet of vertical space is not the vanishing-point for fifty feet of vertical space. That which cuts off the view of the hull beyond the horizon is the horizon itself—the vanishing-line of the surface upon which the vessel sails.
If at the horizon the earth-line is reduced to a vanishing point, and no surface can be seen beyond it, there must be a definite ratio of departure of the visual line beyond the horizon. The amount of vertical space involved in the contraction increases as to the square of the distance, and therefore very nearly conforms to the calculated ratio of the earth's supposed convexity. For this reason, sailors can approximate the distance of a vessel by estimating how much of it is apparently below the horizon. In considering the subject above discussed, do not lose sight of the principles by which the horizon is formed, for herein lies the solution of the whole question of the phenomenon of the receding ship.
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The source scans remain the record. This page preserves the periodical's text as an editorial transcription; its claims remain those of The Flaming Sword.
The Flaming Sword · Vol. 16, No. 33 · Jul 4, 1902 · PDF p. 12