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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: — Have not straight lines been projected by engineers? Is it not a fact that in the construction of long tunnels, that at times the work is carried on from both sides of the mountain, the tunnels meeting midway, and the sides approximating with great accuracy? Is not this the driving of a straight line through solid rock, as it were? If the tunnels be driven from equal altitudes above sea level, and meet in the center, would the completed tunnel—under present engineering practice—be straight, or would it curve in conformity with the curvature of the earth's surface? If straight, could a person using a powerful telescope at one end, directing its axis parallel with the sides, see through the tunnel?—E. S., Philadelphia, Pa.
It is a fact, that engineers and surveyors perform some remarkable feats of accuracy in the construction of tunnels, canals, etc., in leveling, and in geodetic survey. Notwithstanding this, no engineer or surveyor outside of Koreshanity, has ever surveyed an air line. Lines which do not curve either to the right or the left, are frequent results of the work of survey; but the factors of perspective and curvation of visual lines preclude the possibility of extending an air line through space by means of optical instruments. In the great American geodetic survey over the North American continent, the surveyors followed the 39th parallel, but they also followed the curvature of the earth throughout the entire distance. From the basis of this fact, it is quite apparent that surveys as now conducted follow the earth's curvature.
Mining and tunnel surveys do not differ materially in principle from surface surveys; the work of construction of tunnels is but the result of accurate leveling. If tunnels be driven from equal altitudes above sea level or a given datum line, and meet in the center, which they sometimes do, within a very few inches, the opening when completed is level, conforming to the curvature of the earth. This is inevitable because of the methods of survey employed. However complicated such work may be in detail, the principle involved is that of back and foresight surveying, in which foresight is positive and backsight is negative; they neutralize each other, and thus conform to the curvature of the earth, whether that surface be convex or concave. Johnson, in his elaborate work on "Theory and Practice of Surveying" in all its phases, asserts on page 74, that if the back and foresights are equal, "the effect of the earth's curvature is eliminated by so doing, however long the sights may be." There are few grade tunnels, and these are, for the most part, in mines where tunnels follow the veins.
A tunnel 10 or 15 miles in length, perfectly straight like a tube, could be seen through with a telescope, if placed midway between roof and floor, and midway between the sides, because perspective would operate equally on all sides. But this is quite different from surface views, where the solid surface is beneath, and not counterbalanced by a corresponding solid surface above; and quite different also from surface surveys, because geolinear foreshortening operates in surface views in conjunction with vertical perspective, and a horizon is formed, not because the earth is convex, but because, so far as visual lines are concerned, it is practically a plane. The only difference between a view on a plane surface and a view on a concave surface, from the same altitude, would be, that on the latter the horizon would be farther away, and the geolinear extense in view greater; and in proportion to the rapidity of concave curvature, the more the retinal picture of the view would elongate.
The average depression per mile may be considered as 8 inches per mile. To be strictly accurate, a new ratio would be necessary for, say, every hundred miles or so, because the quarter circumference must be equal in depression to the earth's radius. The same results would be obtained with reference to the rise of surface in a concave earth. The common rule applies for all ordinary purposes of observation and experiment within the range of vision, even from high altitudes.
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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. 15, No. 17 · 15 Mar. 1901 · PDF pp. 12-13