TWILIGHT, the interval during which the atmosphere is illuminated after sunset; formerly known as crepusculurn, Lat. for dusky or obscure. The analogous early morning phenomenon is known as the dawn (q.v.). These phenomena are caused by the intervention of the atmosphere between the sun and the earth's surface. An entire absence of atmosphere would cause darkness to set in sharply at sunset as on the moon; but under present conditions even when the sun is some distance below the horizon the upper layers of air are illuminated and are reflecting light. Even as early as the 11th century the duration of twilight was determined as ending when the sun had "travelled" 18° below the horizon and subsequent observations have not materially modified the figure.
This quantity, 18°, has been made the measure for the interval between sunset or sunrise and "complete" darkness, and is termed astronomical twilight; but during a large part of this interval the light is insufficient for ordinary employments, consequently a shorter period, civil twilight, is also recognized for which the quantity is about 6°, but it is conditioned by the amount of light still available. The duration in each case is dependent on the latitude of the observer and the season of the year. The intensity of illumination depends to a con siderable extent on the amount of atmospheric cloud and dust. Twilight after the sunsets of 1883-85 was frequently intense on account of the reflection from the extra dust in the higher layers of the atmosphere as a result of the eruption of Krakatoa.
The duration and possibility of astronomical twilight may be geometrically exhibited as follows : let 0 be the position of the observer; Z the zenith; P the pole of the heavens; ADB, the plane of the horizon ; FDE, the path of the sun. Let the circles ADB and FDE intersect in the points D and which thus corre spond to sunrise and sunset. Astronomical twilight prevails dur ing the period between the sun's position on the horizon and when it is 18° below the horizon; the arcs ZC and ZCI equal 108°, and terminate on the circle FDE at C and then the arcs DC and D represent the distance to be traversed by the sun during twilight and the arc represents the sun path dur ing "complete" darkness, and its path during the "day."
To calculate CD, join CP by an arc of a great circle, then in the triangle ZPC, ZP = the colatitude of 0; PC = the sun's polar distance and ZC =108°. The angle ZPC, the sun's hour angle, then gives the time before or of ter noon when the sun passes C or The times of sunrise and sunset being known, the dura tion of dawn and twilight is a matter of simple subtraction. This represents the problem when the sun does attain a depression of 18°, but this depression may not be attained. Take ZG equal to 108°. Now if G lies beyond B and E (the maximum depression of the sun), E being also below B, then the sun will rise and set, but never descend so low as to occasion "complete" darkness and the entire interval between sunset and sunrise will be twi light.
If E be not below B but above it, the sun will never descend below the horizon, i.e., will neither rise nor set, and so will give the phenomenon known as the midnight sun. Since the new PE = 9o° —sun's declination, and PG = latitude of observer+18°, then for there to be "complete" darkness the latitude of the ob server together with the declination of the sun must exceed 72°. The maximum declination of the sun is about 23° 3o', and hence in latitude 72° —23° 30'=48° 3o' there will be one day without a true night ; in higher latitudes there will be an increasing number of such days ; and in lower latitudes none. In mid-England there is no real night from about May 22 to July 22. To calculate the duration of civil twilight ZC and are made equal to 96° and the argument then proceeds as above.