. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. ides ZP, AP,and the opposite angle A, to find the angle ZPA, or thehour angle of A ; and the angle PZA, or the azimuth fromthe north. Orin the triangle ZPB,the data are the sides ZP, BP,and the opposite angle B, to find the angle ZPB, the hourangle of B, and BZP, the azimuth. Cor. 1. In the same triangle ZAP, or ZBP, the co-al-titude ZA3 or ZB, at the same time, may be found. 494 MATHEMATICS. Cor. 2. If the co-altitude ZA
. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. ides ZP, AP,and the opposite angle A, to find the angle ZPA, or thehour angle of A ; and the angle PZA, or the azimuth fromthe north. Orin the triangle ZPB,the data are the sides ZP, BP,and the opposite angle B, to find the angle ZPB, the hourangle of B, and BZP, the azimuth. Cor. 1. In the same triangle ZAP, or ZBP, the co-al-titude ZA3 or ZB, at the same time, may be found. 494 MATHEMATICS. Cor. 2. If the co-altitude ZA, or ZB be given insteadof the latitude, the co-latitude ZP may be determined in thesame triangle ZAP, or ZBP. PROBLEM XXI. Given the latitude of the place, and the dcclhiaticn of a star ;to fmd the tbne,xvhen its apparent diurnal motion is perpen-dicular to the horizon* Let yx be the parallel,described by the star ; anddraw the vertical circle Zh,touching it at o. Nowwhen the star is at o, itsmotion is perpendicular tothe horizon. And in theright-angled spheric trian-gle ZPo, the data are ZP= the co-latitude, and Po= the co-declination, tofind Z. ZPo, the hour v! O Therefore, as R : tang. oP :: cot. PZ : cos. ZPo ;that is, R : cot. dec. :: tang. hit. : cos. ZPo ; which,converted into time, is the time from the stars being onthe meridian. Hence the time, when the star is on the me-ridian, being found, the required time may be determined. Note 1. The tinac, when a fixed star is on the meridian,may be found thus : Subtract the suns right ascension for the given day fromthe stars right ascension, increased by 24- hours, if necessa-ry ; the remainder is the approximate time of the stars be-ing on the meridian. As 24h. : the dailv change of the suns right ascension ::the approximate time : a fourth number ; which being sub- SPHERIC ASTRONOMY. 4,95 traeted from the approximate time, the remainder is the truelime.* Note 2. The time of a fixed stars being on the merid-ian, toge
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