|Transposition from Geometrical to Mechanical Principles.||www.rolf-keppler.de
When we transpose the geometrical principles under consideration to mechanics, we have to deal with material surfaces and angles instead of geometric lines which bound figures on paper; the principles are the same, for geometry treats of the relations of form of material things.
of the Air Line. Starting from Naples Dock, goini South alon the Gulf Coast.
Upper View, looking East; lower view looking West
When we carry our demonstrations from the realm of principles to principles applied, we do no violence to our conclusion. Such transposition is necessary to demonstrate the truth about the material form of the earth, or the character of its tangible contour.
The principles of right angles constitute the basis of mechanics as well as of geometry.
Every mechanic considers right angles; he works with the square. The laws of these relations of form must be obeyed alike by the builder, engineer, and surveyor.
If we place two mechanic's squares in line, the perpendicular arms will be parallel, and may be closely fitted together. It also follows that if we place the perpendicular arms together, the horizontal blades will form a straight line; the result are identical. Two rectangular metal plates accurately trimmed and placed edge to edge will force the other sides to form a straight line, as in the accompanying diagram.
If two plates joined will form a straight line, it follows that in the adjustment of three plates, the result would be the same; the same result would be invariable for every subsequent adjustment.
Ten thousand plates joined would form a continuous rectiline.
A straight line would be forced because of the fact that at every junction the surfaces joined would be parallel, with the horizontals at right angles; consequently the horizontals would necessarily be in line, Flagstones upon pavements running for miles, are illustrations of the principles involved.
If such squares laid in a straight line will join accurately the contiguous surfaces, it follows that if the surfaces were joined accurately, the pavement would extend in the
same direction-in a straight line. There is no possible escape from this conclusion.
We may further illustrate this principle by reference to the survey of railroad tangents, which often extend for miles in a straight line, as related to the right and the left.
These tangents are surveyed by means of the transit instrument, a small telescope mounted in a horizontal axis, and made to revolve perpendicularly. The instrument may be taken one mile from a given point, and adjusted so that the signal staff is coincidental with the perpendicular cross-hair.
Four-mile R.R. Tangent Surveyed by Revolving Transit on Horizontal, Riht-angled Axis-Perpendicular View
As the instrument has a fixed axis
at right angles with the line of vision, or horizontal axis of the tube,
if the tube be revolved on its right-angled axis so as to point in the
opposite direction, another staff, two miles from the first, may be placed
exactly in line with the first staff and the line of collimation extending
through the tube.
In the accompanying diagram, presenting a view of the ground from the vertical, A is the point of the first staff; B, the telescope, CD, its axis at right angles with the line X; E is the point of the second staff, and Y is the new line extended from B, by revolving the telescope perpendicularly on its axis CD.
If the axis be true, the lines X and Y will form a continuous
straight line two miles in length, its extension being dependent upon a right-angled axis only three inches from either side of the line!
If such long distances can be connected together by so short a right-angled axis, it follows that if surfaces of rectangles of greater adjusting leverage are placed in conjunction, they are capable of extending absolutely straight lines.
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