Let the place be in the Northern hemisphere; then if the complement of the latitude be greater than (the depression) 18 degrees, subtract 18 degrees from it, and the remainder will be the Sun’s declination North, when total darkness ceases. But if the complement of the latitude is less than 18 degrees, their difference will be the Sun’s declination South, when the twilight begins to continue all night. If the latitude is South, the only difference will be, that the Sun’s declination will be on the contrary side.
Thus at London, when the Sun’s declination North is greater than 20½ degrees, there is no total darkness, but constant twilight, which happens from the 26th of May to the 18th of July, being near two months. Under the North Pole the twilight ceases, when the Sun’s declination is greater than 18 degrees South, which is from the 13th of November, ’till the 29th of January: So that notwithstanding the Sun is absent in this part of the world for half a year together, yet total darkness does not continue above 11 weeks; and besides, the Moon is above the horizon for a whole fortnight of every month throughout the year.
Prob. XXV. The day of the Month be given; to find those places of the Frigid Zones, where the Sun begins to shine continually without setting; and also those places where he begins to be totally absent.
Bring the Sun’s place to the meridian, and mark the number of degrees contained betwixt that point and the equator; then count the same number of degrees from the nearest Pole (viz. the North Pole, if the Sun’s declination is Northerly, otherwise the South Pole) towards the equator, and note that point upon the meridian; then turn the globe about, and all the places which pass under the said point, are those where the Sun begins to shine constantly, without setting on the given day. If you lay the same distance from the opposite Pole towards the equator, and turn the globe about, all the places which pass under that point, will be those where the longest night begins.
The Latitude of the place being given, to find the hour of the day when the Sun shines.
If it be in the summer, elevate the Pole according to the latitude, and set the meridian due North and South; then the shadow of the axis will cut the hour on the Dial plate: For the globe being rectified in this manner, the hour circle is a true Equinoctial Dial; the axis of the globe being the Gnomon. This holds true in Theory, but it might not be very accurate in practice, because of the difficulty in placing the horizon of the globe truly horizontal, and its meridian due North and South.
If it be in the winter half year, elevate the South Pole according to the latitude North, and let the North part of the horizon be in the South part of the meridian; then the shade of the axis will show the hour of the day as before: But this cannot be so conveniently performed, tho’ the reason is the same as in the former case.
To find the Sun’s altitude, when it shines, by the Globe.
Having set the frame of the globe truly horizontal or level, turn the North Pole towards the Sun, and move the meridian up or down in the notches, until the axis casts no shadow; then the arch of the meridian, contained betwixt the Pole and the horizon, is the Sun’s altitude.