TWILIGHT

, in Astronomy, is that faint light which is perceived before the sun-rising, and after sunsetting. The Twilight is occasioned by the earth's atmosphere refracting the rays of the sun, and reflecting them among its particles.

The depression of the sun below the horizon, at the beginning of the morning, and end of the evening Twilight, has been variously stated, at different seasons, and by different observers: by Alhazen it was observed to be 19°; by Tycho 17°; by Rothman 24°; by Stevinus 18°; by Cassini 15°; by Riccioli, at the time of the equinox in the morning 16°, in the evening 20° 1/2; in the summer solstice in the morning 21° 25′, and in the winter 17° 15′. Whence it appears that the cause of the Twilight is variable; but, on a medium, about 18° of the sun's depression will serve tolerably well for our latitude, for the beginning and end of Twilight, and according to which Dr. Long, (in his Astronomy, vol. 1, pa. 258) gives the following Table, of the duration of Twilight, in different latitudes, and for several different declinations of the sun. |

Latitude.	0	10	20	30	40	45	50	52 1/2	55	60	65	70	75	80	85	90
Θ	En-	h	m	h	m	h	m	h	m	h	m	h	m	h	m	h	m	h	m	h	m	h	m	h	m	h	m	h	m	h	m	h	m
ters	<*>	1	18	1	21	1	28	1	41	2	8	2	39	w	n	w	n	w	n	w	n	w	n	c	d	c	d	c	d	c	d	c	d
*p	*w	1	16	1	19	1	25	1	36	1	58	2	19	3	3	w	n	w	n	w	n	w	n	c	d	c	d	c	d	c	d	c	d
<*>		1	13	1	15	1	20	1	28	1	43	1	55	2	12	2	25	2	41	3	55	w	n	w	n	w	n	c	d	c	d	c	d
<*>		1	12	1	13	1	17	1	24	1	35	1	44	1	55	2	2	2	10	2	33	3	8	4	18	w	n	w	n	w	n	w	n
		1	13	1	14	1	18	1	24	1	35	1	43	1	54	2	0	2	8	2	27	2	56	8	41	5	2	17	32	w	n	w	n
		1	16	1	17	1	21	1	28	1	40	1	49	2	1	2	8	2	18	2	43	3	26	11	38	11	14	10	32	8	38	c	n
<*>		1	18	1	19	1	23	1	30	1	43	1	53	2	6	2	15	2	26	2	57	4	4	10	24	9	30	7	46	c	n	c	n

Where c d signify that it is then continual day, c n continual night, and w n that the Twilight lasts the whole night.

In this problem, there are given the sides of an oblique spherical trian- gle, to find an angle; viz, given the side ZP the colatitude of the place; PΘ the codeclination, or polar distance; and ZΘ the zenith distance, which is always equal to 108°, viz, 90° from the zenith to the horizon, and 18° more for the sun's distance below the horizon. For example, suppose the place London in latitude 51° 32′, and the time the 1st of May, when the sun's declination is 15° 12′ north. Here then ZP = 38° 28′ the complement of 51° 32′, and PΘ = 74° 48′, the complement of 15° 12′. Then the calculation is as follows.

PΘ =	74° 48′
PZ =	38  28
PΘ - PZ =	36  20	= D
ZΘ =	108  00
ZΘ + D =	144  20	72°	10′ = (1/2) ―(ZΘ + D)
2 )
ZΘ - D =	71  40	35	50 = (1/2) ―(Z○ - D)

Then,
Co-ar. sin. polar dist.	= 74°	48′	0.01547
Co-ar. sin. colat.	= 38	28	0.20617
Sine (1/2) ―(ZΘ + D)	= 72	10	9.97861
Sine (1/2) ―(ZΘ - D)	= 35	50	9.76747
Sum of these four logs.			19.96772
Half sum gives	74° (28 1/2)′		9.98386

Which doubled gives 148 57 for the angle ZPO.

This 148° 57′ reduced to time, at the rate of 15° per hour, gives 9^h 55^m 48^s, either before or after noon; that is, the twilight begins at 2^h 4^m 12^s in the morning, and ends at 9^h 55^m 48^s in the evening on the given day at London.

TWINKLING of the Stars, denotes that tremulous motion which is observed in the light proceeding from the sixed stars.

This Twinkling in the stars has been variously accounted for. Alhazen, a Moorish philosopher of the 12th century, considers refraction as the cause of this phenomenon.

Vitello, in his Optics, (composed before the year 1270) pa. 449, ascribes the Twinkling of the stars to the motion of the air, in which the light is refracted; and he observes, in confirmation of this hypothesis, that they Twinkle still more when they are viewed in water put into motion.

Dr. Hook (Microgr. pa. 231, &c) ascribes this phenomenon to the inconstant and unequal refraction of the rays of light, occasioned by the trembling motion of the air and interspersed vapours, in consequence of variable degrees of heat and cold in the air, producing corresponding variations in its density, and also of the action of the wind, which must cause the successive rays to fall upon the eye in different directions, and consequently upon different parts of the retina at different times, and also to hit and miss the pupil alternately; and this also is the reason, he says, why the limbs of the sun, moon, and planets appear to wave or dance.

These tremors of the air are manifest to the eye by the tremulous motion of shadows cast from high towers; and by looking at objects through the smoke of a chimney, or through steams of hot water, or at objects situated beyond hot sands, especially if the air be moved transversely over them. But when stars are seen through telescopes that have large apertures; they Twinkle but little, and sometimes not at all. For, as Newton has observed, (Opt. pa. 98) the rays of light which pass through different parts of the aperture, tremble each of them apart, and by means of their various, and contrary tremors, fall at one and the same | time upon different points in the bottom of the eye, and their trembling motions are too quick and confused to be separately perceived. And all these illuminated points constitute one broad lucid point, composed of those many trembling points confusedly and insensibly mixed with one another by very short and swift-tremors, and so cause the star to appear broader than it is, and without any trembling of the whole.

Dr. Jurin, in his Essay upon Distinct and Indistinct Vision, has recourse to Newton's hypothesis of fits of easy refraction and reflection for explaining the Twinkling of the stars: thus, he says, if the middle part of the image of a star be changed from light to dark, and the adjacent ring at the same time be changed from dark to light, as must happen from the least motion of the eye towards or from the star, this will occasion such an appearance as Twinkling.

Mr. Michell (Philos. Trans. vol. 57, pa. 262) supposes that the arrival of fewer or more rays at one time, especially from the smaller or more remote fixed stars, may make such an unequal impression on the eye, as may at least have some share in producing this effect: since it may be supposed that even a single particle of light is sufficient to make a sensible impression on the organs of sight; so that very few particles arriving at the eye in a second of time, perhaps not more than three or four, may be sufficient to make an object constantly visible. See Light.

Hence, he says, it is not improbable that the number of the particles of light which enter the eye in a second of time, even from Syrius himself, may not exceed 3 or 4 thousand, and from stars of the 2d magnitude they may probably not exceed 100. Now the apparent increase and diminution of the light, which we observe in the Twinkling of the stars, seem to be repeated at intervals not very unequal, perhaps about 4 or 5 times in a second. He therefore thought it reasonable to suppose, that the inequalities which will naturally arise from the chance of the rays coming sometimes a little denser, and sometimes a little rarer, in so small a number of them, as must fall upon the eye in the 4th or 5th part of a second, may be sufficient to account for this appearance.

Since these observations were published however, Mr. Michell (as we are informed by Dr. Priestley in his Hist. of Light, pa. 495) has entertained some suspicion, that the unequal density of light does not contribute to this effect in so great a degree as he had imagined; especially as he has observed that even Venus does sometimes Twinkle. This he once observed her to do remarkably when she was about 6 degrees high, though Jupiter, which was then about 16 degrees high, and was sensibly less luminous, did not Twinkle at all. If, notwithstanding the great number of rays which doubtless come to the eye from such a surface as this planet presents, its appearance be liable to be affected in this manner, it must be owing to such undulations in the atmosphere, as will probably render the effect of every other cause altogether insensible.

Musschenbroek suspects (Introd. ad Phil. Nat. vol. 2, sect. 1741, pa. 707) that the Twinkling of the stars arises from some affection of the eye, as well as the state of the atmosphere. For, says he, in Holland, when the weather is frosty, and the sky very clear, the stars Twinkle most manifestly to the naked eye, though not in telescopes; and since he does not suppose there is any great exhalation, or dancing of the vapour, at that time, he questions whether the vivacity of the light, affecting the eye, may not be concerned in the phenomenon.

But this philosopher might have satisfied himself with respect to this hypothesis, by looking at the stars near the zenith, when the light traverses but a small part of the atmosphere, and therefore might be expected to affect the eye most sensibly. For he would have found that they do not Twinkle near so much as they do near the horizon, when much more of their light is intercepted by the atmosphere.

Some astronomers have lately endeavoured to explain the Twinkling of the fixed stars, by the extreme minuteness of their apparent diameter; so that they suppose the sight of them is intercepted by every mote that floats in the air. To this purpose Dr. Long observes (Astron. vol. 1, pa. 170) that our air near the earth is so full of various kinds of particles, which are in continual motion, that some one or other of them is perpetually passing between us and any star we look at, which makes us every moment alternately see it and lose sight of it: and this Twinkling of the stars, he says, is greatest in those that are nearest the horizon, because they are viewed through a great quantity of thick air, where the intercepting particles are most numerous; whereas stars that are near the zenith do not Twinkle so much, because we do not look at them through so much thick air, and therefore the intercepting particles, being fewer, come less frequently before them. With respect to the planets, it is observed that, because they are much nearer to us than the stars, they have a sensible apparent magnitude, so that they are not covered by the small particles floating in the atmosphere, and therefore do not Twinkle, but shine with a steady light.

The fallacy of this hypothesis appears from the observation of Mr. Michell, that no object can hide a star from us that is not large enough to exceed the apparent diameter of the star, by the diameter of the pupil of the eye; so that if a star were even a mathematical point, or of no diameter, the interposing object must still-be equal in size to the pupil of the eye; and indeed it must be large enough to hide the star from both eyes at the same time.

The principal cause therefore of the Twinkling of the stars, is now acknowledged to be the unequal refraction of light, in consequence of inequalities and undulations in the atmosphere.

Besides a variation in the quantity of light, it may here be added, that a momentary change of colour has likewise been observed in some of the fixed stars. Mr. Melville (Edinb. Essays, vol. 2, pa. 81) says, that when one looks steadfastly at Sirius, or any bright star, not much elevated above the horizon, its colour seems not to be constantly white, but appears tinctured, at every Twinkling, with red and blue. Mr. Melville could not entirely satisfy himself as to the cause of this phe- | nomenon; observing that the separation of the colours by the refractive power of the atmosphere, is probably too small to be perceived. Mr. Michell's hypothesis above mentioned, though not adequate to the explication of the Twinkling of the stars, may pretty well account for this circumstance. For the red and blue rays being much fewer than those of the intermediate colours, and therefore much more liable to inequalities from the common effect of chance, a small excess or defect in either of them will make a very sensible difference in the colour of the stars.

TYCHONIC System, or Hypothesis, is an order or arrangement of the heavenly bodies, of an intermediate nature between the Copernican and Ptolomaic; and is so called from its inventor Tycho Brahe. See System.