A method is given for reducing the zenith to the equator and equinox of any standard catalogue, so as to eliminate the reductions of individual stars to the apparent equator and equinox of date. The aberration is handled by an approximate method, but the errors introduced by this are very small. Secondly, the standard coordinates, re-formulae, so that it is no longer necessary to solve explicitly for azimuth and zenith distance for each star. The number of references per star to seven figure trigonometrical tables is reduced by this from eleven to three, and the total amount of computation is correspondingly cut down. The refraction is handled by an approximate method, but the approximation is in fact better than that which has been used so far. Plate constants obtained in this way are converted to constants suitable for the actual azimuth by a single operation which comprises allowances for (a) baseline azimuth, (b) azimuth change due to precession and nutation, (c)zero error due to aberration, (d) scale error due to aberration,(e) scale error due to refraction, (f) lack of perpendicularity of the measuring machine. It is considerably simpler to apply these corrections to the plate constanta than it is to apply them to the coordinates of each star separately.
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