Prob. XX. To find in what Latitude the longest Day is, of any given length, less than 24 hours.
Bring the solstitial point to the meridian, and set the index to 12 at noon; then turn the globe Westward, ’till the index points at half the number of hours given; which being done, keep the globe from turning round its axis, and slide the meridian up or down in the notches, ’till the solstitial point comes to the horizon, then that elevation of the Pole will be the latitude.
If the hours given be 16, the latitude is 49 degrees; if 20 hours, the latitude is 63¼ degrees.
Prob. XXI. A place being given in one of the Frigid Zones (suppose the Northern) to find what number of Days (of 24 hours each) the Sun doth constantly shine upon the same, how long he is absent, and also the first and last Day of his appearance.
Having rectified the globe according to the latitude, turn it about until some point in the first quadrant of the ecliptic (because the latitude is North) intersects the meridian in the North point of the horizon; and right against that point of the ecliptic on the horizon, stands the day of the month when the longest day begins.
And if the globe be turned about ’till some point in the second quadrant of the ecliptic cuts the meridian in the same point of the horizon, it will shew the Sun’s place when the longest day ends, whence the day of the month may be found, as before: Then the number of natural days contained between the times the longest day begins and ends is the length of the longest day required.
Again, turn the globe about, until some point in the third quadrant of the ecliptic cuts the meridian in the South part of the horizon; that point of the ecliptic will give the time when the longest night begins. Lastly, turn the globe about, until some point in the fourth quadrant of the ecliptic cuts the meridian in the South point of the horizon; and that point of the ecliptic will be the place of the Sun when the longest night ends.
Or, the time when the longest day or night begins, being known, their end may be found by counting the number of days from that time to the succeeding solstice; then counting the same number of days from the solstitial day, will give the time when it ends.