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.
"In surveying for any extensive work, it is necessary to take account of the departure of the surface of the earth from an optical level or plane surface. It is always done in surveying for water works and the like, else the water would not follow the ways laid out for it."—Editor Notes and Queries Dept., Scientific American, April 1, 1905.
"1. In running levels for a waterway of considerable length, like the Panama canal, is not the rotundity of the earth an important factor that must be considered? A.—In running levels for waterways of considerable length the line which is actually run is substantially a circle whose center is the center of the earth. The sites [sights?—ED.] taken by the instrument between successive settings are so short that the curvature of the earth does not appreciable affect them, and at each new setting of the instrument the line of the level is parallel to the circumference of the earth at that point."—Editor Notes and Queries Dept., Scientific American, April 15, 1905.
The confusion of the mind of the scientific world on points directly related to the subject of the shape of the earth, is clearly reflected in the above quotations referring to the survey of waterways. In the first quotation it is affirmed that it is always necessary to make allowance for the curvature of the earth when surveying for water works and levels; while in the second quotation, written and published only two weeks later, it is affirmed that the surveyed level itself conforms to the arc of the earth's curvature, for the reason that the sights taken by the instrument are so short that the curvature does not appreciable affect them.
If so much confusion prevails regarding the factors of surveying, how can it consistently be said that surveyors have again and again demonstrated the earth's convexity? If the surveyors do not themselves know whether or not they make allowance for the earth's curvature, how can they say they determine the actual direction of the curvature of the earth's arc?
We have treated the subject of making allowance for the earth's curvature in past issues. Students of surveying in the schools are told that such allowance is made. It belongs for the most part to the theoretical side of surveying. It must be considered in order to make the facts fit in the theory that the earth is convex. There are many surveyors and civil engineers who do all kinds of practical surveying, who hold that no such allowance is made in fact.
They work day after day without taking the earth's curvature into consideration at all, for the reason that their methods of surveying neutralize or offset the effect of the curvature, whether it be considered as convex or concave.
From the theoretical point of view, that which seems to be allowance made for convex curvature is nothing more nor less than the combined factors of perspective foreshortening, visual curvilineation, and atmospheric refraction. There is a seeming allowance made in surveying for water works, where the most exact leveling is employed; but it is due to an optical factor which about covers the accredited ratio of curvature, minus supposed refraction. The shape of the earth cuts no more figure in the work of surveying than does the theoretical side of astronomy in the work of prediction of eclipses.
In another column we publish in full a reply by the Editor of the Notes and Queries Department of the Scientific American, to several questions relative to what would necessarily obtain if the earth were convex. The answers to questions 2 and 3 we reverse completely. If it were possible to stretch a wire across a lake ten miles in width, the wire might touch the water at either shore, and in the middle be about 16⅔ feet above the surface of the lake. We know this would be the case, not only because it is a certain conclusion from the basis of the earth's known concavity, but because we have definitely and accurately surveyed such a line, and have thereby absolutely demonstrated that a rectiline over the earth's surface is not tangent to a convexity, but sustains the relation of a chord to the concave arc.
Again, an absolutely straight tunnel ten miles in length, constructed through a mountain range as described in the article referred to—the tunnel terminating on either side on a level with the plane, would be 16⅔ feet higher in the middle than at the entrances. The tunnel would not extend below the level of the plane, but above it. If the tunnel were absolutely level, it would be in the form of a concave arc, and if water were admitted to the tunnel, it would cover the entire floor at a uniform depth. But if the floor of the tunnel were absolutely straight, the middle being higher would cause the water to flow toward the entrances of the tunnel, because it would be down hill all the way from the middle to the entrance on either side. This is exactly the reverse of what would be the case if the earth were convex, for then the highest portions of the tunnel would be the entrances, and the middle the lowest portion.
In much the same way that the processes of ordinary surveying and leveling are generally supposed to indicate the earth's convexity, geodetic survey is supposed to add abundant testimony in favor of the popular belief. The ideas of the public are very hazy on all these subjects. The geodetic lines follow the earth's curvature across the continents, no matter whether they be convex or concave. The work of the geodeists is not a test of the direction of the earth's curvature. They determine the earth's ratio of curvature by indirect processes—from the area embraced in their triangles and quadrilaterals.
Geodetic survey determines the size of the earth and the fact that it is spherical; but there are no methods employed in the old geodesy to determine whether the surface on which we live be convex or concave. Geodesists have demonstrated conclusively that the earth is not flat; and they are satisfied to conclude, without the warrant of facts, that because it is not flat it is convex. We maintain and demonstrate that it is concave.
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The Flaming Sword · Vol. 18, No. 47 · · PDF p. 12