Flaming Sword Archive · Vol. 17, No. 2 · Nov 1902

The Survey of a Level Line

A reader asks how a level-line survey and frozen-water tests bear on terrestrial curvature; the editorial answer defines a level line and describes the Koreshan geodetic experiment.

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.

Editor Flaming Sword :— (i ) I have conversed with a friend of mine regarding the Cellular Cosmogony or hollow globe theory. He offers as a proof of the popular theory of the earth’s convexity what he affirms to be a fact; viz., that if a company of surveyors going east from Colorado to the plains of Kansas, and running a level line with a transit, they would run out into the air, and consequently above the ground. How is this to be explained ? Has such a survey ever been made? I presume it is only a supposition. (2) Has the curvature of the earth ever been determined by testing the frozen surface of any large body of water? When attending school in New York State years ago, I heard a teacher telling how the rotundity of the earth had been settled by tests on the ice, and found to be eight inches to the mile.—F. W. L., Colorado Springs, Colo.

(1) In answering this question, we must define a level line. It is conceded by all that still water is level. A still body of water is at rest— its surface is smooth; and it must conform to the general contour of the earth, whether that contour be convex, flat, or concave. The surface of water is at right angles to the direction of gravity at every point. If the perpendiculars converge beneath the surface, the water is convex; if the perpendiculars are all parallel, the water is flat; but if the perpendiculars converge above us, as we have demonstrated they do, the surface of water is concave. Now, a level line is parallel or coincidental with the surface of still water.

Scanned PDF p. 11 from The Flaming Sword, Nov 1902.
Scanned PDF p. 12 from The Flaming Sword, Nov 1902.

The earth being a concave sphere, a level line curves concavely, and the surface of all water is concavely level — and this is in accordance with the etymology of the word level, which is from a root meaning to rise or raise up. To elevate means to lift up; to levy is to raise or collect, as for debt, tax, etc.; a levee is an embankment; levity is lightness, or tendency to go up; a lever is that with which we lift weights. Therefore, a level surface is one which, as related to any particular point, curves upward; a level surface is a natural concave static plane. This is the meaning which inheres in the primary root from which level is derived. A concave level line is therefore not a straight line, but a line parallel or coincidental with the true concave water level.

The sea level is taken as the general datum line in the survey of all land elevations. Water is comparatively smooth, while land is not so. Running across the American continent from east to west, say, on the thirty-ninth parallel, north latitude, there is a gradual ascent from the level of the Atlantic to the Alleghany mountains; from thence a descent to the Mississippi river; from thence, an ascent to the Rockies; then a plateau to the Sierra Nevadas, and then the Pacific slope. Now, if a company of surveyors, starting from a point in Colorado, say, 7,000 feet above sea level, should undertake to run an unbroken level line eastward to the plains of Kansas, they would run off the land into the air, for the simple reason that the level line would continue to be parallel with the sea level, always 7,000 feet above sea level, while the Kansas plains would slope downward toward the east. From Colorado to the Mississippi there is a gradual descent; and a departure of the level line from the land surface would be the natural and inevitable result of the eastward slope; and on the other hand, if the level line were started at a given altitude from the Kansas plains westward, it would in due course run into the ground at a distance proportionate to the altitude of the starting point and the slope of the plains.

Well informed surveyors understand this; and only those who are not at all posted as to the principles of geodetic and geologic survey would think of using such facts as an argument in favor of the earth’s convexity; for if, as in the case above, running eastward would prove convexity, running westward would as surely (?) prove concavity. While it is true that such a survey as noted above has never been made,— in just the way cited,— surveyors can determine where such a line would extend; but the methods they employ are too intricate to detail in this Department; they are set forth in any authoritative work on geodetic surveying.

(2) The surface of either ice or water was never tested to determine the direction of the earth’s contour, by any definite method, until the Koreshan Unity inaugurated its Geodetic Expedition in the year 1897. The convexity of the earth has never been settled by anybody, for the simple reason that it is not convex, and scientists know that there is no definite proof that it is so; they assume that it is convex. There are two general methods employed in ascertaining the ratio of the earth’s curvature: First, by measuring the length of degrees of latitude and longitude; and second, by geodetic surveying, which enables surveyors to determine ratio or curvature from computation of the area of surveyed triangles and quadrilaterals. The hollow globe 8,000 miles in diameter contains the same surface area as would a convex body of same diameter.

Koreshan Scientists made the first survey in the history of the world for the purpose of determining the direction of the curvature of the surface upon which we live; we have demonstrated that this surface is concave, curving about 8 inches to the mile. We did not project a level line, but a straight line which, in the middle of the chord, was at right angles to the perpendicular. The line was a chord of arc. The water level was the arc of the concave level; the chord was the rectiline which projected into the water at a distance proportionate to the altitude of the line at the middle of the chord.

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