Set the quadrant over both Stars at the observed degrees of altitude, and keep it fast upon the globe with your fingers; then slide the meridian up or down in the notches, ’till the quadrant cuts the given azimuth in the horizon; that elevation of the Pole will be the latitude required.
Prob. XLIII. Having the Latitude of the place, to find the degree of the Ecliptic, which rises or sets with a given Star; and from thence to determine the time of its Cosmical and Achronical rising and setting.
Having rectified the globe for the latitude, bring the given Star to the Eastern side of the horizon, and mark what degree of the ecliptic rises with it: Look for that degree in the wooden horizon, and right against it, in the kalendar, you will find the month and day when the Star rises Cosmically. If you bring the Star to the Western side of the horizon, that degree of the ecliptic which rises at that time, will give the day of the month when the said Star sets Cosmically. So likewise against the degree which sets with the Star, you will find the day of the month of the Achronical setting; and if you bring it to the Eastern part of the horizon, that degree which sets at that time will be the Sun’s place when the Star rises Achronically.
Thus, in the latitude of London, Syrius, or the Dog-Star, rises Cosmically the 10th of August, and sets Cosmically the 10th of October. Aldebaran, or the Bull’s Eye, rises Achronically on the 22d of May, and sets Achronically on the 19th of December.
Prob. XLIV. Having the Latitude of the place, to find the time when a Star rises and sets Heliacally.
Having rectified the globe for the latitude, bring the Star to the Eastern side of the horizon, and turn the quadrant round to the Western side, ’till it cuts the ecliptic in 12 degrees of altitude above the horizon, if the Star be of the first magnitude; then that point of the ecliptic which is cut by the quadrant, is 12 degrees high above the Western part of the horizon, when the Star rises; but at the same time the opposite point in the ecliptic is 12 degrees below the Eastern part of the horizon, which is the depression of a Star of the first magnitude, when she rises Heliacally; or has got so far from the Sun’s beams, that she may be seen in the morning before Sun-rising. Wherefore look for the said point of the ecliptic on the horizon, and right against it will be the day of the month when the Star rises Heliacally. To find the Heliacal setting, bring the Star to the West side of the horizon, and turn the quadrant about to the Eastern side, ’till the 12th degree of it above the horizon, cuts the ecliptic; then that degree of the ecliptic which is opposite to this point, is the Sun’s place when the Star sets Heliacally.
Thus you will find that Arcturus rises Heliacally the 28th of September, and sets Heliacally December the 2d.