. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . spheroidal figure of the earth is taken into consideration. Let P A P B, Fig. 3229, be the meridians of A and B, the earth being considered as a spheroid ; letA M, B N, be the normals to the surface meeting the polar axisin M and N; join B M. Suppose A^B to be the surface of asphere whose centre is M, and radius M A. Then, because thearc A B is very small, and A M is a normal to the spheroid, it isnearly equal to the radius of curvature at A, therefore thes
. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . spheroidal figure of the earth is taken into consideration. Let P A P B, Fig. 3229, be the meridians of A and B, the earth being considered as a spheroid ; letA M, B N, be the normals to the surface meeting the polar axisin M and N; join B M. Suppose A^B to be the surface of asphere whose centre is M, and radius M A. Then, because thearc A B is very small, and A M is a normal to the spheroid, it isnearly equal to the radius of curvature at A, therefore thesurface of the sphere will very nearly pass through B, and thedifference between the arc A ß on the sphere and on the sphe-roid will be altogether insensible. The spherical triangle p A Bmay be considered as that whose solution we have just given,and on this supposition B Mj9 = 90° — V is the colatitude of the true colatitude of B is the angle B N P = 90° — L,which is greater than B M P by the angle M B N. Let I — V = \r — L = MBN = ^; we have then, in the triangle B M N, C M - 0 N sm. (p MNBM sin. B N M BM COS. L ;. but C M = A M . e2 sin. /, C N = B N . e^ sin. L, therefore sin. (p = e^ COS. L BM sin. I BNBM sin. L )■ And since z^-=-^ and :^-r^ differ from unity by a quantity of -a very minute order, we havesin. (p = e^ COS. L (sin. I — sin. L), very nearly. Now, sin. L = sin. {^ — (A + ^) ] = sin. ^ - (A + <^) cos. /, nearly. Also, sin. (p =nearly ; therefore (p = e^ (x + ^) cos. L cos. L Hence, transposing and dividing, <p, very e^ A COS. L COS. I 1 — e^ COS. L COS. (p =z e^ A /, nearly, and A + ^Hence, on the spheroid, the difference of latitude A tan. e- A COS. L cos. /, nearly ; A (1 + e^ I). i-lu = T) COS. A D^ sinr sin. 1 2 r^ sin. tan. l^ + è 0, [15] where r = A M, the normal to the surface at the station A. The same things being given, to find the difference of longitude.—The difference of longitude onthe sphere
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Keywords: ., bookcentury1800, bookdecade1870, bookidsp, booksubjectengineering
