A manual of spherical and practical astronomy, embracing the general problems of spherical astronomy, the special applications to nautical astronomy, and the theory and use of fixed and portable astronomical instruments, with an appendix on the method of least squares . N CIRCLE. In Fig. 48, constructed as in Art. 123, let 0 be the position of the star. The great circle describedby the telescope is NZS\ and Z isthe zenith of the instrument. Thearc AO drawn from the pole of thegreat circle NZS to the star inter-sects this circle in 0, and 00 re-presents the micrometer thread whichbisects the st
A manual of spherical and practical astronomy, embracing the general problems of spherical astronomy, the special applications to nautical astronomy, and the theory and use of fixed and portable astronomical instruments, with an appendix on the method of least squares . N CIRCLE. In Fig. 48, constructed as in Art. 123, let 0 be the position of the star. The great circle describedby the telescope is NZS\ and Z isthe zenith of the instrument. Thearc AO drawn from the pole of thegreat circle NZS to the star inter-sects this circle in 0, and 00 re-presents the micrometer thread whichbisects the star, since this thread isalso perpendicular to the plane of theinstrument, and OO =^ c is the dis-tance of the star from the collimationaxis. If the telescope were directed to the pole, the threadwould coincide with PP^ P being the point in which the greatcircle AP intersects NZS. Hence, P is the apparent pole ofthe instrument, and the apparent polar distance of the star, asgiven by the instrument, is P0*= 90°—o(denoting the in-strumental declination by 3). But, since the triangle PAO isright angled at P and 0, the angle PAO is measured byPO. We have, therefore, in the triangle PAO (with the nota-tion of Art. 123), the sides PA = 90° — ??, ^0 = 90° + c, PO. 90 ^, with the angle APO = 90° + r — m, and the angle PAO = 90° — d. Hence, by Sph. Trig., sin d =cos d sin (t — m) = cos d COS (t — 771) = sin n sin c -{- cos n cos c sin d \cos n sin c -f sin n cos c sin d s. (191)cos c cos d ) in which d is the corrected declination,* r is the east hour angleof the star, and 7n and ?i are the instrumental constants as deter-mined by transit observations (Art. 151). But, since n is exceed-ingly small (seldom more than = ) and c not more than15 even when the star is observed near one of the extremetransit threads, the product sin c smn will be insensible, and wemay always put cos n ^ 1. The first and third of these equa-tions, therefore, become whence sin 8 = cos c si
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