[Fig. 28] shows a part of the earth surrounded by such a dust-laden atmosphere, which is illuminated on the left by the rays of the sun, but which, on the right of the figure, lies in the shadow cast by the earth. To an observer placed at 1 the sun is just setting, and all the atmosphere above him is illumined with its rays, which furnish a bright twilight. When, by the earth's rotation, this observer has been carried to 2, all the region to the east of his zenith lies in the shadow, while to the west there is a part of the atmosphere from which there still comes a twilight, but now comparatively faint, because the lower part of the atmosphere about our observer lies in the shadow, and it is mainly its upper regions from which the light comes, and here the dust and moisture are much less abundant than in the lower strata. Still later, when the observer has been carried by the earth's rotation to the point 3, every vestige of twilight will have vanished from his sky, because all of the illuminated part of the atmosphere is now below his horizon, which is represented by the line 3 L. In the figure the sun is represented to be 78° below this horizon line at the end of twilight, but this is a gross exaggeration, made for the sake of clearness in the drawing—in fact, twilight is usually said to end when the sun is 18° below the horizon.
Let the student redraw [Fig. 28] on a large scale, so that the points 1 and 3 shall be only 18° apart, as seen from the earth's center. He will find that the point L is brought down much closer to the surface of the earth, and measuring the length of the line 2 L, he should find for the "height of the atmosphere" about one-eightieth part of the radius of the earth—i. e., a little less than 50 miles. This, however, is not the true height of the atmosphere. The air extends far beyond this, but the particles of dust and vapor which are capable of sending sunlight down to the earth seem all to lie below this limit.
The student should not fail to watch the eastern sky after sunset, and see the shadow of the earth rise up and fill it while the twilight arch retreats steadily toward the west.
Fig. 29.—The cause of long and short twilights.
Duration of twilight.—Since twilight ends when the sun is 18° below the horizon, any circumstance which makes the sun go down rapidly will shorten the duration of twilight, and anything which retards the downward motion of the sun will correspondingly prolong it. Chief among influences of this kind is the angle which the sun's course makes with the horizon. If it goes straight down, as at a, [Fig. 29], a much shorter time will suffice to carry it to a depression of 18° than is needed in the case shown at b in the same figure, where the motion is very oblique to the horizon. If we consider different latitudes and different seasons of the year, we shall find every possible variety of circumstance from a to b, and corresponding to these, the duration of twilight varies from an all-night duration in the summers of Scotland and more northern lands to an hour or less in the mountains of Peru. For the sake of graphical effect, the shortness of tropical twilight is somewhat exaggerated by Coleridge in the lines,
"The sun's rim dips; the stars rush out:
At one stride comes the dark."
The Ancient Mariner.
In the United States the longest twilights come at the end of June, and last for a little more than two hours, while the shortest ones are in March and September, amounting to a little more than an hour and a half; but at all times the last half hour of twilight is hardly to be distinguished from night, so small is the quantity of reflecting matter in the upper regions of the atmosphere. For practical convenience it is customary to assume in the courts of law that twilight ends an hour after sunset.
How long does twilight last at the north pole?