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The theory and practice of surveying. Designed for the use of surveyors and engineers generally, but especially for the use of students in engineering (1886)

Johnson, J. B. (John Butler), 1850-1902 · New York, J. Wiley & sons · leaf 653

An illustration from The theory and practice of surveying. Designed for the use of surveyors and engineers generally, but especially for the use of students in engineering, 1886, leaf 653 — ons. It is desirable to find the length of the line nl, of the normal nm, andof the radius of curvature ftr, all in terms of e, L, and a. Also to findthe geocentric latitude in terms of a, b, and L. To find nl, we have nl=V nd2 + d?= |/^ + y~r For the ellipse, dy _ Pxtdx a*y whence «/= |/y + ** =… … (3) Fig. 153. Squaring, remembering thaty = nl sin L, we have, after reducing, a(i-*2) nl = (I — e1 sin2 L)i (A) To find the length of the normal nm = N, we have ww : nl .. x: dl. But whence — dy P dl = nd tan dnl = y -— = — x = (1 — <r) x ; d!r as nm = N — nl 1 — £2 (1 — ^sin^Z)^ .... (4). • •…

Surveying

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