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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.
Editor Flaming Sword: — Having come into possession of some of the Koreshan publications, I confess to somewhat of an interest in the subjects of which you treat. Would you be willing to answer the following questions? (1) If the theory of measuring distances by angles is correct, how is it possible to blunder to the extent of millions of miles in the measuring of planetary distances? (2) If the distance to the sun from the surface of the earth is but a few thousand miles, would not observations taken at two different points on the earth's surface show practically an equilateral triangle? (3) Why is a mountain that is entirely within the range of a telescope, hidden from view by an intervening mountain of less altitude? (4) Can a ship which is hull down, so called, be brought wholly within the range of vision by a telescope? (5) If perspective foreshortening is the cause of the disappearance of the hull, why does not the vessel disappear all at once? If you will kindly answer these questions you will confer a favor on me.—\ \ \*
In modern astronomy the earth is considered to be a convex body, rotating on its axis and revolving about the sun; it is held that the earth is a planet, and that planets are projectiles in space, related to a common center of gravity. From the basis of these assumptions, all of the errors of calculation of the distance and magnitude of the heavenly bodies have arisen; and necessarily, misconceptions concerning the proportions and relations of the solar system are due to astronomical ignorance concerning the earth's place in the universe. The entire question is made to depend primarily upon the shape of the earth, and its relation to the sun, for observations are made from the surface upon which we live.
Geometry is exact, and the principles of triangulation are definite; the results of calculation from the basis of actual triangles or quadrilaterals may be obtained with precision. But if we take a false hypothesis as a working basis of astronomical measurements, our triangles will be hypothetical, not real; or, an assumption may lead to giving false values to observed angles. It is certain that a perpendicular ray of gravity is at right angles to the horizontal. If the earth were convex, all perpendiculars would converge beneath the earth's surface and diverge upward into space.\* On the basis of the supposition that all perpendiculars do so diverge upward and outward, the lunar paralactic angle (about 60′) would make the distance to the moon amount to 60 times the length of the earth's radius. If, however, observations of the moon are actually made from the basis of a concave arc, the same parallax would have a wholly different value, making the moon's distance only about 800 miles from the earth's surface.
The assumed distance from the earth to the sun is taken as a unit in measuring the distance to the planets and stars. While the process of measuring the distance to the sun is more complicated than that of computing the distance to the moon, the principle is practically the same—that of horizontal parallax, applied from the basis of the primary assumption of the earth's convexity. The astronomer's process of measuring planetary distances involves the arrangement of planetary orbits in a diagram; the mapping of the results of at least two observations of the position of a planet at intervals separated by the time of its sidereal period; and the construction of lines connecting the sun and planet and two points on the earth's orbit.
If the planet is a superior planet, the lines bound a quadrilateral; the major axis being a direct line connecting the sun and the planet, the minor axis being the length of the planet's elongation or difference between the right ascension of the planet and the sun. Now, it is obvious that if no such relations exist in the solar system—that is, if the earth be not a planet—the angles to which the astronomer has given values do not exist; they are purely hypothetical, and the values entirely fictitious. The blunder is the result of an error at the very beginning of the application of the process, which has for its basis a false assumption.
(2) The central sun is located at the center of the concave cell. Two perpendiculars extending from the center, and a base line 4,000 miles in length, form an equilateral triangle; but it must be remembered that a perpendicular at any point passes through the zenith. The central sun is invisible; we see only the outermost projection, which is only about 900 miles from the earth's surface in the region of the equator. In the Koreshan Astronomy we deal with curved angles in measuring solar, lunar, and planetary distances. Light is not propagated in straight lines in universal space; and in accounting for phenomena, one must consider the actual factors and the true principles of physics and optics, else optical and mental illusion will be the result.
(3) A distant mountain is hidden from view by one much nearer and of less altitude, first, because of the angle which the latter subtends; second, because vision does not extend in straight lines, but curves upward and outward away from the surface; and third, because of the principles of perspective and geolinear foreshortening. All objects on the earth's surface when viewed from any point or altitude, conform in their general lateral relation to the arc of the surface which appears to be convex; and all objects beyond the horizon seem to be lower than they really are. A telescope would not reveal the mountain that is hidden, for the reason that it would magnify the intervening one in proportion to the telescopic power. If the lines of vision were straight, and if it were possible to observe objects in the distance without the operation of the principles of foreshortening, the most distant mountain would appear to be higher than the intervening one; but we must consider all the factors, principles, and laws by which we perceive objects, as well as their apparent relation.
(4) There is a distinct horizon apparent to the unaided eye, and there is still another and more distant horizon apparent through a telescope, from same altitude of observation. Any object situated on the water's surface between the two horizons may be clearly seen by the telescope. Thus, if the vessel is hull down, or even half-mast down, in clear atmosphere and on calm sea, it may be wholly restored by means of the telescope. These statements are not conjectural; they are the result of hundreds of specific and comparative observations.
(5) A receding balloon in open space apparently contracts equally on all sides, and is finally reduced to the vanishing point; this is due to perspective foreshortening. The lower part of a receding ship disappears first, and the space occupied by the vessel apparently contracts more rapidly at the bottom; this is due to the combined factors of perspective and geolinear foreshortening. The ship is sailing upon a surface, which for purposes of illustration we may consider to be perfectly flat. Upon the retina of the eye of an observer standing upon the beach, the first mile of the geolinear extense produces a picture of definite length; the second mile contracts about 6 times more rapidly, and the third mile about 18 times more rapidly than the first, while the angle subtended by the fourth mile is so small that it fails to make an impression.
The result of this geolinear foreshortening, or the apparent drawing of the surface toward the observer, is a definite horizon on a level with the eye; beyond the horizon no surface can be seen because the horizon is the vanishing-line for a definite amount of lateral space above the water, and that vanishing-line proves to be as effectual a barrier to the visual perception of objects on the water beyond the horizon, as the supposed convex bulge. If the space vanished is 6 feet, that much of the hull of the outgoing vessel disappears; but the vanishing-point of 6 feet is not the vanishing point of 40 or 50 feet; hence the sails remain in sight. The restoration of the hull of the vessel by means of the telescope is proof that the disappearance of the hull is due to optical factors, and that the apparent bulge on the water is an optical illusion.
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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 Flaming Sword · Vol. 16, No. 10 · 24 Jan. 1902 · PDF pp. 12-13