Seasonal Variations in Daylight, Twilight, and Darkness

Abstract

r1-HE diurnal and seasonal variations in daylight, and darkness are rather difficult to comprehend without the aid of apparatus or graphic devices. These diagrams and tables were designed to visualize and emphasize some of the facts relating to but they may prove to be of more general interest. The tables upon which the present brief study is based appeared in General Tide Tables for the Year 1916, published by the U. S. Coast and Geodetic Survey. This publication contains the only table giving the time of beginning of morning (or dawn), and of the end of evening which the writer found available. It should be noted that the tables are constructed as a practical aid to the mariner, the supposition being that the observer's eye is 15 feet above the surface of the sea (or the plane of the land). The sunrise and sunset tables give the time of appearance and disappearance of the upper limb (not the center) of the sun, as actually seen from an elevation of 15 feet above the horizon. At any moment it is daylight over slightly more than half the earth; if the fringe on which the sun is either rising or setting be included, at least a portion of the sun is above the horizon over 50.8 per cent of the earth's surface. Not all of the remaining 49.2 per cent is enveloped in total darkness, however. Approximately I5.4 per cent of the total surface lies in the belt of astronomical twilight, which is lighted to a greater or lesser degree by the refracted rays of the sun when it is not more than 18? (by the usual definition) below the horizon. The belt of twilight is only one-third as wide, comprising the zone within which the sun is not more than 6? below the horizon, approximately 4.4 per cent of the earth's surface. Total darkness, so far as the sun is concerned, envelops only about 34 per cent of the earth's surface at any moment and grades off insensibly through the toward daylight. The formula used in computing the mean local civil time of sunrise and sunset takes into consideration the latitude, the sun's declination, and the sun's zenith distance. The latter is used as a constant, with a value of 90? 56' o9, the excess above 9go being due principally to the refraction of the sun's rays in the horizon (36' 29) and to the sun's semidiameter (I6' oi), allowance also being made for the sun's horizontal parallax (o' 09, subtracted), and for the dip of the horizon for a height of I5 feet (3' 48). Variations of refraction in the horizon produce a sensible change in the time of rising or setting of the sun, but it is impossible to estimate these variations in advance. Under extreme changes in atmospheric temperature and pressure, refraction in the horizon may vary about 8' either way from the mean value used in the formula, but this would make only a few seconds difference in the time of sunrise or sunset near the equator. It would, however, amount to a whole minute of time in latitude 48? at the time of the local summer solstice, to two minutes in latitude 6I?, and would increase rapidly toward the pole. There are also differences in the duration of sunlight for the forenoon and afternoon of the same day which, in higher latitudes, amount at times to more than half an hour. Close study of the detailed tables furthermore reveals minor variations between comparable dates, as in times of sunrise and sunset at the time of the two equinoxes in points of opposite and equal latitude. 656