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 EDITOR.
Leveling not a Proof of Convexity.
Editor Flaming Sword:—I am trying to interest a gentleman in the Koreshan Cosmogony, and he has propounded the following question: If the earth is concave, how is it possible for engineers to calculate correctly the connection of two rivers by a canal, so that they reach the proper water level from river to river? For instance, the Raritan canal, which connects the Delaware and Raritan rivers. The canal is at least 25 miles long—yet the water level was calculated accurately so that the canal made correct connections between the rivers. The gentleman referred to says that were the earth concave, the engineers' calculations would have been untrue, and when the canal met the rivers it would have been away out. This, he thinks, proves that the earth is convex; otherwise, why were the engineers' calculations correct—which was proved by the actual digging of the canal according to their ideas?—M. K., Brooklyn, N. Y.
Such questions as the above can best be answered by giving the actual facts of canal surveying and engineering; for the work of constructing canals is a "proof" that the earth is convex to those only who have nothing more than school-book knowledge of the processes employed.
We cannot conceive that any one familiar with the principles of ordinary leveling should offer the fact that such work is accurately executed, as constituting a genuine proof of the correctness of the popular conceptions concerning the shape of the earth. There are some men graduating from modern institutions of learning, even young surveyors with only a theoretical knowledge of surveying, who are ready to affirm that engineers demonstrate the theory of the earth's convexity every time they construct a canal or dig a tunnel; but their minds are disabused of such conceptions, or rather deceptions, when they have spent a few years in practical work along these lines.
Surveyors and engineers perform their work, not according to a theory of the earth's shape, but upon the basis of experience; and their calculations are made from the facts of actual measurements. If they entertained no theory whatever of the earth's contour, the results of their calculations would be the same; and further, it would make no difference in the results if the earth were flat instead of either convex or concave, for the engineer's datum line is the level line—that is, a line to which standing water would conform. If the earth were flat, the water level would be straight; if convex, the level would be a convex arc; if concave, it would follow that the water level is concave.
Now, the object of the engineer or surveyor in laying out a canal is to determine a continuous datum line throughout the length of the canal. The instrument he employs is the spirit level, and every time he levels his instrument its axis is parallel to his datum line. He works upon the land; it is his business to determine how far above his datum line is each one of his bench-marks. When he has done this, the contractor knows just how deep to make his excavations at every point along the route of the canal.
Accurate leveling for canals is accomplished by what is known as the back and foresight method of surveying. The principles of this method are simple. If the work were conducted upon an absolutely level surface, with the instrument leveled and adjusted always at the same height, the line surveyed would be parallel to the surface, even if the line surveyed were a thousand miles long. This would be inevitable, since at each setting of the instrument it is leveled and the back and foresight made equal; the line could neither depart from nor approach the earth. But surveys are made upon uneven surfaces; for this reason rods and targets, with scale of feet and inches, are used to enable the surveyor to determine exactly how far his every bench-mark is above his datum line. He does this by keeping a record of each reading, and when he has reached a bench-mark he takes the difference between the sum of his foresights and the sum of his back sights, and this gives him the elevation of his bench-mark as related to a bench-mark already passed. By tallying his bench-mark elevations he can determine his datum line.
Let it be remembered that the datum line must be parallel to the water-level, which must conform to the general contour of the earth; therefore, if the earth is concave, the datum is concave also. The surveyor works upon a concave surface, not with reference to a datum which is straight, but one which is curved; and he follows the curve by virtue of the fact that he levels his instrument and makes his back and foresights equal.
By this method "the effect of the earth's curvature" is eliminated; this is most emphatically stated to be the case by authorities on this subject, which we might quote if necessary. If the convex curvature may be entirely ignored in such work, it should not be difficult for the logical mind to perceive that the route of the canal with its datum line may be accurately surveyed and its bed accurately excavated by those who are in utter ignorance of the fact that the earth is concave.
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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. 47 · Oct 10, 1902 · PDF p. 12