Twilight

Twilight is a lengthening out of the day after the sun has sunk below the horizon, or before he rises above it, and is caused by the reflection of light by the atmosphere. It is the same sort of thing as occurs in mountainous districts, where the peaks reflect light into the valleys below when the sun is below the horizon as seen from the valley. It has been found that twilight will be enjoyed at every place till the sun has sunk 18° below the horizon; if the sun is moving vertically, therefore, he will soon traverse that distance, and the twilight will be of short duration, If, however, he is travelling in a plane cutting the horizon at a much smaller angle, he will take longer to get 18° below it, for he will have to travel farther in his own path, and consequently twilight will last longer. Let H Z P R represent the meridian of a place in the northern hemisphere. The circle H O R O' at right angles to the meridian will represent the horizon, and Z will be the zenith. If P P' be the axis of the earth, Z P will be 90° minus the latitude of the place, for if E Q be the equator E Z is the latitude. Now, the sun's daily path is in a circle parallel to the equator. During the summer months the circle will be north of the equator, so let M M' represent it, the points O O' being the points of intersection of horizon and solar path. Draw an arc, Z T, cutting the horizon at L, such that L T is 18°; then, since Z L is, of course, 90°, Z T, is 108°. Twilight then lasts while the sun is moving from T to O; from O to O' the sun is above the horizon, so it is a day; from O' to a point T' (corresponding to T) it is evening twilight; and from T' to T it is night. We know the sun's polar distance, P T, as we know what days of the year we are considering; Z P is the 90° latitude, and Z T is 108°, so we can calculate the angle Z P T by spherical trigonometry. This gives us the time at which twilight will begin; so, knowing the time of sunrise, we can subtract the one from the other and find the duration of twilight. If Z M' were 108°, then absolute night would not exist, for twilight would last the whole time from sunset to sunrise. This is the case in the latitude of London during a few nights in June on either side of the longest day. In latitude 48° 30' there is one night - June 21st - when only twilight exists. In this case the sun has reached his most northern limit, so M' Q = 20° 30', P R = 48° 30', and since P Q = 90° it follows that R M' = 90° minus (23° 30' + 48° 30'). Hence R M' = 18°, which is just the limit of twilight. Below latitude 48° 30' there can be no such vanishing night, but in higher latitudes the number of such nights increases, until we get to the point when twilight, too, ceases, and the sun itself actually shines all night. The length of this continuous day increases as we approach the pole, but is balanced by the continuous night of the winter months. in the tropics the sun rapidly sinks below the horizon, and twilight lasts only about an hour.