. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . , and equal to twice the value of —r—, which the spheroid would have if it were homogeneous, that is, ^^ + 7 = ^ ¿ • 00865, and 5f = G (1 -f 7 sin.^ 0- [23] GEODESY. 1663 This theorem was first given by Clairaut, and is of great importance in determining the figureof the earth from experiments with the pendulum. With respect to the values given to g, see our article onGunnery. We shall now proceed to show how the figure ofthe earth is to be determined from
. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . , and equal to twice the value of —r—, which the spheroid would have if it were homogeneous, that is, ^^ + 7 = ^ ¿ • 00865, and 5f = G (1 -f 7 sin.^ 0- [23] GEODESY. 1663 This theorem was first given by Clairaut, and is of great importance in determining the figureof the earth from experiments with the pendulum. With respect to the values given to g, see our article onGunnery. We shall now proceed to show how the figure ofthe earth is to be determined from geodetic operations. Weshall, therefore, first consider the difíerent properties of anoblate spheroid, and then compare theni with the resultsdeduced from observation. Let A P a^, Fig. 3234, be an ellipse, which, by its revolu-tion about its minor axis Pj?, generates an oblate A C = a, C P = 6, the eccentricity = a e^ the ordinateM N = y, G^ - X, the normal M r = n, M R = N, theradius of curvature at 11 = p, and the latitude of M, orthe angle M r a = I. Now, the equation to the ellipse is«2 2/2 + 62 .r2 = a? b\. Also y = n sin. I, and a; = — x N r b 62 n cos. Î : a2 n^ + - n^ I a^ 62. conse- quently n = hence 62 And because 62 = a^ (1 — e^), therefore V (a^ I _j_ ¿2 si^_2 i^ «2 I + 62 ^ = a2 (1 - e2 /) .a (1 - e2) V(l - e^ ¡^ a cos. I V(l - ^2 i^ N y = a (1 — e^) sin. IV(l - e^ ^) X cos. Ï V(l - e />)a e2 cos. I CR = V(l - ^2 ^)a ^2 sin. I = N e2 COS. ?,= Ne2 sin. I, V(l-e2sin,2/) -1 _ (2 ^2 _ e4) sin_2 /^ . //I — (2 e^ — e-*) ^ /\ [24][25][26] [27][28][29] a (1 - ^2) 6^ ^ (1-^)I [30] J%ö lengths of two degrees on the meridian in given latitudes heing hiov:n from measurement, it isrequired to determine the polar and equatorial diameters.—Let D, D, be the lengths of two degrees infeet ; /, l\ the latitudes of their middle points ; p, p, the radii of curvature
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