A handbook of practical astronomy for university students and engineers

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1891 Excerpt: ...)' sinT77 h'"' which converges rapidly when t does not exceed 30m, and the star is more than 20 from the zenith, as it will be in sextant double altitudes. If we let 2sinH 2 sin4 it,,_„..-= m,. ' = n, (179) sin I" ' sin " K J and substitute the resulting value of z0 for z in (167), we have If the rate of the chronometer is large it must be allowed for. the lower sign being employed for a star culminating between the zenith and the pole. When a star is observed near the meridian at lower culmination, it is convenient to reckon the hour angle from the lower transit, t in (15) must be replaced by 180 + t, and we obtain cosz = sin sin0--cos5 cos cos t =--cos(p + 0 + cosrf cos 2sin2Jt. Developing this in series as before and substituting the resulting value of z0 for z in (168), we have The entire series of observations is conveniently reduced as a single observation by letting z, m and n in (180) and (181) represent the arithmetical means of the values of these quantities for the individual observations. The values of m and n are tabulated in the Appendix, Table III, with the argument t. An approximate value of p is required in computing A. This may be obtained by the method of § 88, from the observation made nearest the meridian. If the sun is observed the declination is taken from the Nautical Almanac for the instant of each observation in case the observations are reduced separately, and for the mean of the times in case they are reduced collectively. If a star is observed with a sidereal chronometer the hour angles t are the intervals between each observed time and the chronometer time of the star's transit. If a star is observed with a mean time chronometer, the intervals must be reduced from mean to sidereal intervals before ente...