sioned by it, is of a much longer duration: this sufficiently appears from the well-known experiment of a lighted body whirled round in a circle, which needs not make many revolutions in a second, to ap. pear as one continued ring of fire. Hence then it is not improbable, that the number of the particles of light, which enter the eye in a second of time even from Sirius himself, may not exceed three or four thousand; and from stars of the second magnitude, they may therefore probably not much exceed an hundred. Now the apparent increase and diminution of the light, which we observe in the twinkling of the stars, seems to be repeated at not very unequal intervals, perhaps about four or five times in a second: why may we not then 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 fourth or fifth part of a second, may be sufficient to account for this appearance? An addition of two or three particles of light, or perhaps of a single one upon twenty, especially if there should be an equal deficiency out of the next twenty, would I suppose be very sensible; this seems at least probable from the very great difference in the appearance of stars, whose light is much less different than, I imagine, people are in general aware of; the light of the middle-most star in the tail of the great Bear does not, I think, exceed the light of the very small star next to it, in a greater proportion than that of about sixteen or twenty to one; and Monsieur Bouger tells us, in his Traité d'Optique before-mentioned, that he finds a difference in the light of objects of one part in sixtysix sufficiently distinguishable.

It will perhaps be objected, that the rays coming from Sirius are too numerous to admit of a sufficient inequality, arising from the common effect of chance, so frequently as would be necessary to produce this effect, whatever might happen in respect to the smaller stars; but till we know what inequality is necessary to produce this effect, we can only guess at it either one way or the other; there is however another circumstance, that seems to concur in the twinkling of the stars, besides their brightness, and this is a change of colour. Now the red and blue rays being very much fewer, I apprehend, than those of the intermediate colours, and therefore much more liable to inequality from the common effect of chance, may help very much to account for this phenomenon, a small excess

or defect in either of these making a very sensible difference in the colour.

It will now naturally be asked, why the frequency of the changes of brightness should not be often much greater, as well as sometimes less, than that abovementioned, and why the interval of the fourth or fifth, or some such part, should be pitched upon, rather than the fortieth or fiftieth part of a second, or than a whole second, &c. for, according to the length or shortness of the time assumed, the changes that will naturally occur, from the effect of chance, will be smaller or greater in proportion to each other. The answer to this question will, I think, tend to render the above solution more probable, as well as to throw a good deal of light upon the whole subject. The lengths of the times then between the changes of brightness, if I am not mistaken, depend upon the dura tion of the perception before-mentioned, occasioned by the impres sion of the light upon the eye, than which they seem to be neither much longer nor shorter. Whatever inequalities fall within a much shorter time than the continuance of this perception, will necessarily be blended together, and have no effect, but as they compose a part of the whole mass; but those inequalities, which fall in such a manner as that they may be assigned to intervals nearly equal to, or something greater than the continuance of this perception, will be so divided by the imagination, which will naturally follow, and pick them out as they arise.-Phil. Trans. 1767.

N. B. The light of the stars appears to the naked eye to be generally white, being too faint to excite the idea of a particular colour; but when it is concentrated by Dr. Herschel's large speculums, it be◄ comes in various stars of various hues; and indeed to the naked eye some of the stars appear a little redder and others a little bluer. The cause of the twinkling of the stars does not, after all, appear to be fully ascertained: it is referred by other philosophers, and with some probability, to changes which are perpetually taking place in the atmosphere, and which affect its refractive density. It is said that in some climates where the air is remarkably serene, the stars have scarcely any appearance of twinkling.-Editor,

CHAP. XXI.

ON TWILIGHT.

FOR the phænomena of twilight, we are principally indebted to

the light reflected by the atmosphere; when the sun is at a certain distance only below the horizon, he shines on some part of the air immediately visible to us, which affords us a portion of reflected light. The distance at which this may happen has been variously ́estimated, and it is perhaps actually different in different climates, being a little greater in countries near the poles than in those which are nearer the equator; there is also sometimes a secondary twilight, when the parts of the atmosphere, which reflect a faint light on the earth, are themselves indebted for this light to an earlier reflection. Some have assigned 18° as the limit of twilight, and on "this supposition, allowing for refraction, the atmosphere must be "capable of reflecting sensible light at the height of about 40 miles. Mr. Lambert, on the contrary, makes the limit only about 60. The - duration of twilight is greater or less as the sun moves more or less obliquely with respect to the horizon; it is, therefore, shortest near the time of the equinoxes, since the equinoctial intersects the horizon less obliquely than any lesser circle parallel to it.-Young's Nat. Phil. Vol. I. p. 26.

The limit of visible twilight is when the sun is 6 degrees below the horizon. In order to find the time when the twilight is shortest, as Rad: Sin. Lat. : : S. 6o 23o. S. Sun's declination, south. Lambert Photometria, sect. 987. Schroter asserts that Venus has a twilight of more than 4°.-Ueber die Venus, 4to. Enfurt, 1793.

CHAP. XXII

GENERAL ASTRONOMICAL REMARKS,

Fixed Stars.

It is impossible to determine exactly the distance of any of the

fixed stars from the earth; yet we are nevertheless able to draw some conclusions that may tend to illustrate their prodigious re

moteness.

1. The diameter of the earth's annual orbit, which contains at least 160 millions of miles, is but a point in comparison of the distance from the nearest star, which is supposed to be Sirius or the Dog-star. At least this star must be upwards of 6000 times more remote than the sun for if a star should appear through a telescope half a minute broad, which is a pretty sensible magnitude, the true apparent diameter would not exceed 18° 3 minutes, which is less than the six thousandth part of the apparent diameter of the sun; and consequently the sun's distance cannot be one six thousandth part of the star's distance from the earth.

2. Could we advance towards the stars ninety-nine parts out of a hundred of the entire, and have only one part remaining, the stars would appear scarcely larger to us than they do at present; for they would show no otherwise than they do through a telescope which magnifies a hundred fold.

3. Nine parts at least in ten of the space between us and the fixed stars, can receive no greater light from the sun, or any of the stars, than that which the earth has from any of the stars in a clear night.

1

4. Light takes up more time in travelling from the nearest star to the earth, than our sailors in making a West India voyage, which is ordinarily performed in six weeks. Sound would not reach us from the same distance in fifty thousand years; nor a cannon-ball in a much less time: which is easily computed by allowing, according to Sir Isaac Newton, ten minutes for the journey of light from the sun

to the earth; and that sound travels at the rate of about thirteen hundred feet in a second.-Miscellanea Curiosa, Vol. I.

Flamstead, Phil. Trans. 1701, conjectures that he had found an annual paralax of 40" or 45"; the polar distance being greatest in June. Cassiui, A. P. 1717, makes the apparent diameter of Sirius several seconds; this however is denied by Halley, Phil. Trans. 1720.

Supposing Saturn to reflect one-seventh of the light that falls on him, and to be equal in brightness to a star as large as the sun, the distance of the star will be 425100 times as great as that of the suu, and its apparent diameter 0" 16"". Hence we may assume the distance 500000.-Lambert. Photometria.

Michell observes, that a star of 500 times the diameter of the sun ought to recall the particles of light from an infinite distance, and thinks that a sensible effect might be produced by a star 22 times as large in diameter as the sun; the attraction of the sun ought to retard it 94000 in an infinite distance. The light of a star of the sixth magnitude is to that of the sun as one to a hundred billions.-Phil. Trans. 1784.

Some stars, if as remote from each other as Sirius is from the sun, should be 42000 times as far off as Sirius. At this distance Sirius would be scarcely visible.-A cluster of 5000 stars, scarcely visible as a mass by the forty-feet telescope, must be above eleven millions of millious of millions of miles off.-Herschel, Phil. Trans. 1795. 1800.

Barker produces five authorities to show that Sirius was formerly reddish, and even redder than Mars, and proves that it is now white. -Phil. Trans. 1760.

Garcin observes, that at Bender Abassi in Asia, where the air is very pure and dry, the stars have a light absolutely fixed and free from twinkling. A. P. 1743.-Young Nat. Ph. II. 991.

Humboldt, by means of diaphragms, in Herschel's manner, has given the following as the comparative brightness of various stars. Sirius 1, Canopus 98, *Centauri 96, Achernar 94, & Indi 50, ẞ 47, & Toucan 70, a Phoenicia 65, a Pavonis 78, a Gruis 81, ẞ 75, y 58.

Euler makes the light of the sun equal to that of 6560 candles at 1 foot distance, that of the moon to a candle at 74 feet, of Venus to a candle at 421 feet, and of Jupiter to a candle at 1620 feet: