_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? _The Aurora._--One other phenomenon of the atmosphere may be mentioned, only to point out that it is not of an astronomical character. The Aurora, or northern lights, is as purely an affair of the earth as is a thunderstorm, and its explanation belongs to the subject of terrestrial magnetism. CHAPTER VI THE MEASUREMENT OF TIME 52. SOLAR TIME.--To measure any quantity we need a unit in terms of which it must be expressed. Angles are measured in degrees, and the degree is the unit for angular measurement. For most scientific purposes the centimeter is adopted as the unit with which to measure distances, and similarly a day is the fundamental unit for the measurement of time. Hours, minutes, and seconds are aliquot parts of this unit convenient for use in dealing with shorter periods than a day, and the week, month, and year which we use in our calendars are multiples of the day.