Prob. XXII. To find in what Latitude the longest Day is, of any given length less than 182 Natural Days.
Find a point in the ecliptic half so many degrees distant from the solstitial point, as there are days given, and bring that point to the meridian; then keep the globe from turning round its axis, and move the meridian up or down until the aforesaid point of the ecliptic comes to the horizon; that elevation of the Pole will be the latitude required.
If the days given were 78, the latitude is 71½ degrees.
This method is not accurate, because the degrees in the ecliptic do not correspond to natural days; and also because the Sun does not always move in the ecliptic at the same rate; however, such problems as these may serve for amusements.
Prob. XXIII. The day of the Month being given, to find when the Morning and Evening Twilight begins and ends, in any place upon the Globe.
In the [foregoing problem], by the length of the day, we mean the time from Sun-rising to Sun-set; and the night we reckoned from Sun-set, ’till he rose next morning. But it is found by experience, that Total Darkness does not commence in the evening, ’till the Sun has got 18 degrees below the horizon; and when he comes within the same distance of the horizon next morning, we have the first Dawn of Day. This faint light which we have in the morning and evening, before and after the Sun’s rising and setting, is what we call the Twilight. [4] Having rectified the globe for the latitude, the zenith, and the Sun’s place, turn the globe and the quadrant of altitude until the Sun’s place cuts 18 degrees below the horizon (if the quadrant reaches so far) then the index upon the hour circle will shew the beginning or ending of twilight after the same manner as before we found the time of the Sun-rising and setting, in [Prob. 18]. But by reason of the thickness of the wooden horizon, we can’t conveniently see, or compute when the Sun’s place is brought to the point aforesaid. Wherefore the globe being rectified as above directed, turn the globe, and also the quadrant of altitude, Westward, until that point in the ecliptic, which is opposite to the Sun’s place, cuts the quadrant in the 18th degree above the horizon; then the hour index will shew the time when day breaks in the morning. And if you turn the globe and the quadrant of altitude, until the point opposite to the Sun’s place cuts the quadrant in the Eastern hemisphere, the hour hand will shew when twilight ends in the evening. Or, having found the time from midnight when the morning twilight begins, if you reckon so many hours before midnight, it will give the time when the evening twilight ends. Having found the time when twilight begins in the morning, find the time of Sun-rising, by [Prob. 18], and the difference will be the duration of twilight.
Thus at London on the 12th of May twilight begins at three quarters past one o’clock: The Sun rises at about half an hour past four: Whence the duration of twilight now is 2¾ hours, both in the morning and evening. On the 12th of November, the twilight begins at half an hour past six, being somewhat above an hour before Sun-rising.