TWILIGHT. If the earth had no atmosphere, we should be involved in total dark ness from the instant of sunset till the instant of sunrise. The transition from day to night and from night to day, occupies an interval which varies with the latitude and the declination of the sun, and this intermediate stage is called twilight. As long as the sun is not more than 18° below the horizon, its light is reflected by the air and the clouds and vapors' suspended in it, in sufficient quantity to render even distant objects visible. The question of the duration of twilight is, therefore, simply reduced to this : How long, after sunset, or before sunrise, does the sun reach a position 18° below the horizon of a given place 2 And this can be answered easily by calculation in spherical trigonometry, Thus, if Z be the zenith, P the pole of the heavens. ASB the horizon, and MSTN the (small)circle which the sun describes about the pole; there is twilight while the sun moves from 'I' to S, ZT being an arc of 108°. In the spherical triangle ZPT, we know the three sides, for ,ZP is the colatitude of the place, PT the sun's polar tance, and ZT is 108'. Hence we can calculate the angleZPT, which is the sun's hour-angle; and from this we find at once how long before or after noon the sun passes the point T. If ZT' be also 108', we see that it is night while the sun moves from 'I" to T, day while it moves from S (through M, its meridian position) to S', morning twilight from T to S, and evening twilight from S' to T'. Make ZO = 108°, then, if PN be less than PC, but greater than PA, there will be no point of the sun's path (MS'NS) so far as 108° from Z; and therefore the points T and T will not exist. In this case the sun will set and rise, but there will be no night, or, rather, twi light will occupy the whole interval from sunset to sunrise. This cannot occur in low latitudes, but does occur during certain periods of the year in northern and southern countries. For
and our condition is, therefore, that 90°-sun's declination, while greater than the iati• tude, does not exceed it by more than 18°. Or, in a simpler form, the latitude, together with the sun's declination, must lie between 90° and 72'. Now the sun's greatest decli nation is about 23° 30', and therefore, in lat. 48° 30' (72° to 23° 301 there will be one night in the year (at the summer solstice) consisting wholly of twilight; for higher lati tudes, more; and for lower none, Some curious problems on this subject, such as the finding the time of year at which the twilight is longest in a given latitude, were among the early triumphs of the differential calculus. A curious pnenomenon, known as the afterglow, or second twilight, often seen in the Nubian desert, is referred by sir John Herschel to a second reflection of solar light in the atmosphere. Lambert and Others ha 1 previously speculated on the possibility of second and even third twilights, but in their time there was no rec6rded observation of such appearances.
Attempts have been made to deduce from the duration of twilight the height of the earth's atmosphere; and from various measurements which have given results agree ing fairly with each other, 50 m. has been assigned as a probable value. But, till we know more of the law of temperature in the atmosphere, we have no very direct means of testing the correctness of such results. In all probability, they are too small. as, in deed, we might expect, if we suppose the higher regions of the atmosphere to be much attenuated, and, therefore, reflecting little light. Besides. the ignition of meteorites is believed to have taken place at altitudes of more than 50 m.; and auroral arches have been observed at least 60 tn. high.