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.
Do Surveyors Allow for Convexity?
Editor Flaming Sword:— While visiting the Pan-American Exposition at Buffalo, I had a talk with Dr. Cyrus R. Teed about the Koreshan theory of the earth being a concave sphere, and I became very much interested in it. I purchased one of the books entitled The Cellular Cosmogony; and several of my neighbors are interested. I am much taken up with the theory, but I cannot say that as yet I believe it. I want to know more about it, and am seeking for information. How do you account for the fact that in digging canals an allowance of 8 inches to the mile has to be made for the convexity of the earth? I mentioned this fact to Dr. Teed in our discussion with him, but he said that it was not so; however, I have since found that it is so. At that time I could not refute his statements, and probably could not now were he here.— J. E. V., Principal Union School, Lafargeville, N. Y.
Allowance for the earth's convexity, 8 inches to the mile, is made by those who are not practical surveyors; such allowance is made only in the mind. We know that it cannot be made in fact in practical work, because the earth is not convex. Every surveyor knows that an allowance of 8 inches to the mile would not be practicable, because it is considered that atmospheric refraction makes the visual line depart from the earth's surface only about six inches to the mile; so that allowance of the full 8 inches must be considered as entirely out of the question at the very beginning of our consideration of the subject.
Let us suppose that an allowance for some kind of curvature is made in canal surveying and engineering. It is assumed that the earth is convex, and that lines of vision are straight, minus refraction. If we level a transit instrument 6 feet above still water, and observe the horizon through the instrument, the cross-hair will appear to be 2′ above the water horizon. From the basis of this apparent dip of the surface, the surveyor concludes that the earth is convex because of his assumption that the line of vision is practically straight. Let a target be placed in line with the cross-hair at a distance of one mile; the center of the target is found to be 5 or 6 inches higher than the instrument. The only actual fact apparent in such observations is that the line of vision and the earth's surface are not parallel but divergent to the extent of 5 or 6 inches to the mile. We maintain that the visual line curves more rapidly than the earth's concave surface. A diagram of our conception of the relation the visual line sustains to the concavity, appears on page 52 of The Cellular Cosmogony. Now it is certain that if the surveyor were to make long sights in his work of leveling, without employing the back and fore sight method, allowance for curvature would have to be made. It would not be for the earth's convexity, but for the curvature of the visual line from the instrument to the target.
Surveyors and engineers employ a method in which it is not necessary to take any curvature into account. It is the back and fore sight method used in field work, and in geodetic surveying and canal engineering where precise leveling is necessary. Back sights and fore sights eliminate curvature. Datum lines surveyed by this process follow the water level, whether the earth be considered as convex, flat, or concave. Concerning field surveying, Johnson's "Theory and Practice of Surveying," a standard work, says on page 74, that where the back sights and fore sights are equal, no matter how long the sights may be, all error as well as the effect of the earth's curvature is eliminated; that is, without duplicating the observations, a line extended for a hundred miles or more, would follow the level of the earth without making any allowance for curvature at all. The leveling of the instrument at each setting would make this inevitable.
Again, on page 576, in considering precise leveling as applied in geodetic surveying, the surveyor is cautioned to keep the back and fore sights equal between the bench-marks; otherwise there will be an excess which must be eliminated. "The curvature of a level surface would also enter into this excess, but it is usually so small a residual distance that the correction for curvature is quite insignificant. There are, however, three instrumental corrections to be applied for the amount of excess; namely, corrections for collimation, inclination of the bubble, and inequality of pivots." These last do amount to something; and there are involved in them elements of discrepancy which the surveyor may trace to convexity or to other fancied causes with equal consistency.
We believe that there are surveyors who honestly suppose, while they do not deduct a given amount of calculated convexity, that in precise leveling by the back and fore sight method, allowance for curvature is virtually made. The expert surveyor, however, knows that he makes no allowance for that which he does not have to consider in his work. The majority of surveyors deny that allowance for any curvature is made in actual, practical work. In reply to inquiries, the Chief Engineer of the Manchester Ship Canal, constructed a few years ago, gave out the emphatic statement that no allowance for curvature was made in its construction. A number of years ago, engineers perpetrated several blunders in endeavoring to make what is termed allowance for the earth's convexity; as a result, the English House of Lords issued a standing order forbidding allowance for curvature in all surveying and engineering work for the government.
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The Flaming Sword · Vol. 16, No. 11 · Jan 31, 1902 · PDF p. 12