. Elements of theoretical and descriptive astronomy, for the use of colleges and academies. here on the plane of the celestialmeridian, RZHN, of some place. HE isthe celestial horizon at that place, Z thezenith, P the elevated pole, and EQ theequator. Let s represent some circumpolarstar, whose declination is known, at itslower culmination. Let its meridian alti-tude be observed, and corrected for instru-mental errors and refraction. (For all celestial bodies except thesun, the moon, and the planets, the corrections for parallax andsemi-diameter will be inappreciable.) To this corrected altitu
. Elements of theoretical and descriptive astronomy, for the use of colleges and academies. here on the plane of the celestialmeridian, RZHN, of some place. HE isthe celestial horizon at that place, Z thezenith, P the elevated pole, and EQ theequator. Let s represent some circumpolarstar, whose declination is known, at itslower culmination. Let its meridian alti-tude be observed, and corrected for instru-mental errors and refraction. (For all celestial bodies except thesun, the moon, and the planets, the corrections for parallax andsemi-diameter will be inappreciable.) To this corrected altitudeadd the stars polar distance, the complement of the stars knowndeclination. The sum is the altitude of the elevated , orthe latitude. If the circumpolar star is at its upper culmination, as at sthe polar distance is to be subtracted from the corrected altitude. If h! and h denote the corrected altitudes at the upper andthe lower culmination, p and p the corresponding polar dis-tances, and L the latitude, we have evidentlyL = h! — pfL = h+p: whence L = l (h! + h) -f- * (p —p).. LATITUDE. 73 In this formula the value of the latitude does not depend on theabsolute value of either polar distance, but merely on the changeof the polar distance between the two transits, which is usuallyso small as to be neglected. This method, then, is free from anyerror in the declination, and is used at all fixed observatories. 76. Second Method,—When the star is at its upper culmi-nation, it will, in general, be more convenient to find thedeclination of the zenith from the meridian zenith distance ofthe star. Taking the star s, for instance, and denoting itsmeridian zenith distance by z} and its declination by d, we have L = ZQ= Qs - Zs = d-z. (a)For the star s, we have L = Zs + Qs = z + d, (b) and for the star s L = Zs - Qs = z—d. (c)From these three formulae a general rule may be deduced, ap-plicable to the upper culmination of every star. We noticethat in the formulae (a) and (b),
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