CREPUSCULUM

, Twilight; the time from the first dawn or appearance of the morning, to the rising of the sun; and again, between the setting of the sun, and the last remains of day.

The Crepusculum, or twilight, it is supposed, usually begins and ends when the sun is about 18 degrees below the horizon; for then the stars of the 6th magnitude disappear in the morning, and appear in the evening. It is of longer duration in the solstices than in the equinoxes, and longer in an oblique sphere, than in a right one; because, in those cases the sun, by the obliquity of his path, is longer in ascending through 18 degrees of altitude.

Twilight is occasioned by the sun's rays refracted in our atmosphere, and reflected from the particles of it to the eye. For let A be the place of an observer on the earth ADL, AB the sensible horizon, meeting in B the circle CBM bounding that part of the atmosphere which is capable of refracting and reflecting light to the eye. It is plain that when the sun is under this | horizon, no direct rays can come to the eye at A: but the sun being in the refracted line CG, the particle C will be illuminated by the direct rays of the sun; and that particle may reflect those rays to A, where they enter the eye of the spectator. And thus the sun's light illuminating an innumerable multitude of particles, may be all reflected to the spectator at A.— From B draw BD touching the circle ADL in D; and let the sun be in the line BD at S: Then the ray SB will be reflected into BA, and will enter the eye, because the angle of incidence DBE is equal to the angle of reflection ABE: And that will be the first ray that reaches the eye in the morning, when the dawning begins; or the last that falls upon the eye at night, when the twilight ends: for when the sun goes lower down, the particles at B can be no longer illuminated.

Kepler indeed assigns another cause of the crepusculum, viz, the luminous matter or atmosphere about the sun; which, arising near the horizon, in a circular figure, exhibits the crepusculum; in no wise, he thinks, owing to the refraction of the atmosphere.— The sun's luminous atmosphere indeed, though neither the sole nor principal cause of twilight, may lengthen its duration, by illuminating our air, when the sun is too low to reach it with his own light. Gregor. Astr. lib. 2, prop. 8.

The depth of the sun below the horizon, at the beginning of the morning, or end of the evening twilight, is determined in the same manner as the arch of vision; viz, by observing the moment when the air first begins to shine in the morning, or ceases to shine in the evening; then finding the sun's place for that moment, and thence the time till his rising in the horizon, or from his setting in it in the evening. It is now generally agreed that this depth is about 18 degrees upon an average.—Alhazen found it to be 19°; Tycho, 17°; Rothmann, 24°; Stevenius, 18°; Cassini, 15°; Riccioli, in the equinox in the morning 16°, in the evening 20° 30′; in the summer solstice in the morning 21° 25′, in the winter solstice in the morning 17° 25′.

Nor is this difference among the determinations of astronomers to be wondered at; the cause of the crepusculum being inconstant: for, if the exhalations in the atmosphere be either more copious, or higher, than ordinary; the morning twilight will begin sooner, and the evening hold longer than ordinary: for the more copious the exhalations are, the more rays will they reflect, consequently the more will they shine; and the higher they are, the sooner will they be illuminated by the sun. On this account too, the evening twilight is longer than the morning, at the same time of the year in the same place. To this it may be added, that in a denser air, the refraction is greater; and that not only the brightness of the atmosphere is variable, but also its height from the earth: and therefore the twilight is longer in hot weather than in cold, in summer than in winter, and also in hot countries than in cold, other circumstances being the same. But the chief differences are owing to the different situations of places upon the earth, or to the difference of the sun's place in the heavens. Thus, the twilight is longest in a parallel sphere, and shortest in a right sphere, and longer to places in an oblique sphere in proportion as they are nearer to one of the poles; a circumstance which affords relief to the inhabitants of the more northern countries, in their long winter nights. And the twilights are longest in all places of north latitude, when the sun is in the tropic of cancer; and to those in south latitude, when he is in the tropic of capricorn. The time of the shortest twilight is also different in different latitudes; in England, it is about the beginning of October and of March, when the sun is in the signs and . For the method of determining it by trigonometry, see Gregor. Astron. lib. 2, prob. 41. See also Robertson's Navigation, book 5, prob. 12.—Hence, when the difference between the sun's declination and the depth of the equator is less than 18°, so that the sun does not descend more than 18° below the horizon; the crepusculum will continue the whole night, as is the case in England from about the 22d of May to the 22d of July.

Given the latitude of the place, and the sun's declination; to find the beginning of the morning, and end of the evening twilight.—In the oblique-angled spherical triangle ZPS, are given ZP the colatitude, PS the codeclination, and ZS = 108°, being the sum of 90° the quadrant and 18° the depression at the extremity of the twilight. Then, by spherical trigonometry, calculate the angle ZPS the hour-angle from noon; which changed into time, at the rate of 15° to the hour, gives the time from noon at the beginning or end of twilight. See Robertson, ubi supra.

Of the Height of the sensible Atmosphere, as determined from the duration of twilight, see Keil's Astron. Lect. lect. 20, pa. 235, ed. 1721; or Long's Astron. vol. 1, pa. 260; where it is determined that the height where the atmosphere is dense enough to reflect the rays of light, is about 42 miles.

, the new moon, which, as it begins to recede from the sun, shews a small rim of light, terminating in horns or points, which are still increasing, till it becomes full, and round in the opposition.

The term is sometimes also used for the same sigure of the moon in her wane, or decrease, but improperly; both because the horns are then turned towards the west, and because the figure is on the decrease; the crescent properly signifying increase, from cresco, I grow.

CRONICAL. See Acronical.