. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . ions have been entertained with respect to the relative merits of the theodoliteand the repeating circle. The French have imagined that they could attain any degree of accuracywith the circle, and that all errors of division and errors ofobservation might be entirely annihilated by repetition. When the angles are measured with a theodolite, no cor-rection is required on account of the different altitudes oftlie signals, as it is the horizontal angle which i
. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . ions have been entertained with respect to the relative merits of the theodoliteand the repeating circle. The French have imagined that they could attain any degree of accuracywith the circle, and that all errors of division and errors ofobservation might be entirely annihilated by repetition. When the angles are measured with a theodolite, no cor-rection is required on account of the different altitudes oftlie signals, as it is the horizontal angle which is observedwith the instrument; but when the sextant or repeatingcircle is employed, the oblique angles are observed, and thesemust be reduced to the plane of the horizon. To reduce the oblique angles to the plane of the horizon.—Let 0, Fig. 3226, be the place of the observer, MON theangle observed between two signals M, N ; Mm, Nn, two vertical lines meeting the horizontal plane m O n in the points m, n. Let 0 Z be a vertical linepassing through O, and with the centre O and radius 1 conceive a sphere to be described, and let 5 N 2. 1652 GEODESY. the planes Z O M, Z 0 N, M O N, cut this sphere in the great circles 0 A, 0 B, A B. The angleobserved with the repeating circle is the oblique angle MON, which is measured by the arc AB,but the required angle is m O n, which is equal to the spherical angle 0. The angles M O m, N O w,are known from observation, and therefore the complements of these angles, or the arcs CA, C B,are known. We have then, in the triangle C A B, the three sides C A, 0 B, A B, given to find theangle 0. Let h, h, be the altitudes of the two signals M and N, 6 the angle between them ; also, let thehorizontal angle =ze + x; then C A = 90° - /i, CB = 90° - A, AB = Ö, angle C = d + x. By ^ . ^ COS. AB — COS. C A COS. C B x« . x ^o^- ^ — ^i^- ^ ^^^- ^ Trig., COS. C = .—^-i—-.—7T^ , or cos. (9 + x) = ^ sin. 0 A sm. OB cos. h cos. h Now, in practice, h
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Keywords: ., bookcentury1800, bookdecade1870, bookidsp, booksubjectengineering
