The time between the index at either of these two positions, and the hour of 6; or half the difference between the oblique ascension and descension is the _Ascensional Difference_.
If the place be in North latitude and the declination of the given point be (North/South) the ascensional difference reduced into time, and (added to/subtracted from) 6 o’Clock, gives the _Semi-diurnal Arch_; the complement whereof to a semicircle, is the _Semi-nocturnal Arch_. If the place be in South latitude, then the contrary is to be observed with respect to the declination.
The semi-(diurnal/nocturnal) arch being doubled, gives the time of continuance (above/below) the horizon. Or the time of continuance above the horizon, may be found by counting the number of hours contained in the upper part of the horary circle, betwixt the place where the index pointed when the given point was in the Eastern or Western parts of the horizon. If the given point was the Sun’s place, the index pointed the time of his rising and setting, when the said place was in the Eastern and Western parts of the horizon, as in _Prob. 18_. Or the time of Sun-rising may be found by adding or subtracting his ascensional difference, to or from the hour of six, according as the latitude and declination are either contrary or the same way.
Thus, at _London_, on the 31st of _May_, the _Sun’s_
_Amplitude_ is 24 degrees Northerly. _Oblique Ascension_, 20. _Oblique Descension_, 58. _Ascensional Difference_, 19. _Semi-diurnal Arch_, 109. His continuance above the horizon, 14½ hours. Sun rises at three quarters past four. Sun sets a quarter past seven.
These things for the Sun vary every day; but for a Fixed Star the day of the month need not be given, for they are the same all the year round.
In the latitude of 51½ North, _Syrus_’s _Amplitude_ is about 28 degrees Southerly. _Oblique Ascension_, 121. _Oblique Descension_, 75. _Ascensional Difference_, 23. _Semi-diurnal Arch_, 67. Continuance above the horizon, 9 hours.
PROB. XXXVIII. _The Latitude and the Day of the Month being given; to find the Hour when any known Star will be upon the meridian, and also the time of its rising and setting._
Having rectified the globe for the latitude of the Sun’s place, bring the given Star to the meridian, and also to the East or West side of the horizon, and the index will shew accordingly when the Star _culminates_, or the time of the _rising_ or _setting_.