Topographic surveying; including geographic, exploratory, and military mapping, with hints on camping, emergency surgery, and photography . ost intricateshore line and contains many islands, all heavily its 45 miles of outline were mapped on a scale of i^ inchesto a mile by one topographer and one stadiaman, both inboats, in 12 days. 104. Stadia Formula with Perpendicular Sight. ^—Insighting the rod from the telescope, the stadia-wires appear 244 STADIA TACHYMETR Y. to be projected upon the rod, thus intercepting a fixed dis-tance upon it. In fact there is formed at the position of
Topographic surveying; including geographic, exploratory, and military mapping, with hints on camping, emergency surgery, and photography . ost intricateshore line and contains many islands, all heavily its 45 miles of outline were mapped on a scale of i^ inchesto a mile by one topographer and one stadiaman, both inboats, in 12 days. 104. Stadia Formula with Perpendicular Sight. ^—Insighting the rod from the telescope, the stadia-wires appear 244 STADIA TACHYMETR Y. to be projected upon the rod, thus intercepting a fixed dis-tance upon it. In fact there is formed at the position of thestadia-wires an image of the rod which the wires intercept,and at points which are the respective foci of the two pointssubtended on the rod. If the object-glass be considered asimple bi-convex lens, then, by the principle of optics, therays from any point of an object converge to a focus at astraight line which is a secondary axis connecting the pointwith its image and passing through the center of the point of intersection of the secondary axis is the opticalcenter. It follows that the lines cC and bB, Fig. j^, drawn. o ^ Fig. 76.—Stadia Measurement on Horizontal. from the stadia-wires, will intersect the object at pointscorresponding to those which the wires cut on the image ofthe rod. From this follows the proportion da p — = —; hence a = -^a,pi t (2) in which d = the distance of the rod from the center of theinstrument;/ = the distance of the stadia-wires from the center of the objective;a = the distance intercepted on the rod by the stadia-hairs; andt = the distance of the stadia-hairs apart. PIf / remained the same for all lengths of sight, then — STADIA FORMULA WITH PERPENDICULAR SIGHT. 245 Avould equal a constant, and d would be directly proportionalto a. Unfortunately / varies with the length of the sight,and the relation between d and a is therefore variable^Representing the principal focal length by the letter /, andapplying the general formul
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