its coming on at a, and going off at n, it appears as Apparent small as a thread, the thin edge being then all that we Motions Heavenly

see.

of the

These spots have made us acquainted with a very Bodies. important phenomenon, namely the rotation of the sun upon its axis. Amidst the changes which these spots are continually undergoing, regular motions may be detected, agreeing exactly with the motion of the surface of the sun, on the supposition that this luminary revolves round an axis almost perpendicular to the ecliptic in the same direction with its motion in its orbit round the earth. By a careful examination of the motion of these spots, it has been ascertained that the sun turns round its axis in about 25 days and a half, and that its equator is inclined to the ecliptic about 70.5.

The spots on the sun's disk are almost always confined to a zone, extending about 30°.5 on each side of the equator. Sometimes, however, they have been observed at the distance of 39°.5 from the equator of the sun.

Bouguer demonstrated, by a number of curious experiments on the sun's light, that the intensity of the light is much greater toward the centre of the sun's disk than towards its circumference. Now, when a portion of the sun's surface is transported by the rotation of that luminary from the centre to the circumference of his disk, as it is seen under a smaller angle, the intensity of its light, instead of diminishing, ought to increase. Hence it follows, that part of the light which issues from the sun towards the circumference of his disk, must be somehow or other prevented from making its way to the earth. This cannot be accounted for, without supposing that the sun is surrounded by a dense atmosphere, which, being traversed obliquely by the rays from the circumference, intercepts more of them than of those from the centre which pass it perpendicularly.

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of the

Heavenly

Apparent ceeded by a facula, or spot brighter than the rest of Motions the disk, the place where it was is soon after not distinguishable from the rest. Bodies. In the Philosophical Transactions, vol. xiv. Dr Wilson, professor of astronomy at Glasgow, hath given a dissertation on the nature of the solar spots, and mentions the following appearances. 1. When the spot is about to disappear on the western edge of the sun's limb, the eastern part of the umbra first contracts, then vanishes, the nucleus and western part of the umbra remaining; then the nucleus gradually contracts and vanishes, while the western part of the umbra remains. At last this disappears also; and if the spot .remains long enough to become again visible, the eastern part of the umbra first becomes visible, then the nucleus; and when the spot approaches the middle of the disk, the nucleus appears environed by the umbra on all sides, as already mentioned. 2. When two spots lie very near to one another, the umbra is deficient on that side which lies next to the other spot: and this will be the case, though a large spot should be contiguous to one much smaller; the umbra of the large spot will be totally wanting on that side next the small one. If there are little spots on each side of the large one, the umbra does not totally vanish; but appears flattened or pressed in towards the nucleus on each side. When the little spots disappear, the umbra of the large one extends itself as usual. This circumstance, he observes, may sometimes prevent the disappearance of the umbra in the manner above mentioned; so that the western umbra may disappear before the nucleus, if a small spot happens to break out on that side.

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Mr Dunn's account.

In the same volume, p. 337. Mr Wollaston observes, that the appearances mentioned by Dr Wilson are not constant. He positively affirms, that the faculæ or bright spots on the sun are often converted into dark ones. "I have many times (says he) observed, near the eastern limb, a bright facula just come on, which has the next day shown itself as a spot, though I do not recollect to have seen such a facula near the western one after a spot's disappearance. Yet, I believe, both Yet, I believe, both these circumstances have been observed by others; and perhaps not only near the limbs. The circumstance of the faculæ being converted into spots, I think I may be sure of. That there is generally (perhaps always) a mottled appearance over the face of the sun, when carefully attended to, I think I may be as certain. It is most visible towards the limbs, but I have undoubtedly seen it in the centre; yet I do not recollect to have observed this appearance, or indeed any spots, towards the poles. Once I saw, with a twelve inch reflector, a spot burst to pieces while I was looking at it. I could not expect such an event, and therefore cannot be certain of the exact particulars; but the appearance, as it struck me at the time, was like that of a piece of ice when dashed on a frozen pond, which breaks to pieces and slides in various directions." He also acquaints us, that the nuclei of the spots are not always in the middle of the umbræ ; and gives the figure of one seen in November 13th 1773, which is a remarkable instance to the contrary. Mr Dunn, however, in his new Atlas of the Mundane System, gives some particulars very different from the above. "The face of the sun (says he has frequently many large black spots, of various forms and dimensions, which move from east to

of the Heavenl Bodies.

tions.

70

west, and round the sun, according to some observa- Apparen tions in 25 days, according to others in 26, and accord- Motion ing to some in 27 days. The black or central part of each spot is in the middle of a great number of very small ones, which permit the light to pass between them. The small spots are scarce ever in contact with the central ones: but, what is most remarkable, when the whole spot is near the limb of the sun, the surrounding small ones form nearly a straight line, and the central part projects a little over it, like Saturn in his ring." Dr Herschel, with a view of ascertaining more ac- Herschel's curately the nature of the sun, made frequent observa- observations upon it from the year 1779 to the year 1794. He imagines that the dark spots on the sun are mountains on its surface, which, considering the great attraction exerted by the sun upon bodies placed at its surface, and the slow revolution it has upon its axis, he thinks may be more than 300 miles high, and yet stand very firmly. He says, that in August 1792, he examined the sun with several powers from 90 to 500; and it evidently appeared that the dark spots are the opaque ground or body of the sun; and that the luminous part is an atmosphere, which, being interrupted or broken, gives us a view of the sun itself. Hence he concludes, that the sun has a very extensive atmosphere, which consists of elastic fluids that are more or less lucid and transparent; and of which the lucid ones furnish us with light. This atmosphere, he thinks, is not less than 1843, nor more than 2765 miles in height; and, he supposes, that the density of the luminous solar clouds need not be much more than that of our aurora borealis, in order to produce the effects with which we are acquainted. The sun then, if this hypothesis be admitted, is similar to the other globes of the solar system, with regard to its solidity-its atmosphere-its surface diversified with mountains and valleys-its rotation on its axis-and the fall of heavy bodies on its surface; it therefore appears to be a very eminent, large, and lucid planet, the primary one in our system, disseminating its light and heat to all the bodies with which it is connected.

Dr Herschel has lately given up the use of the old terms such as spots, nuclei, penumbræ, &c. and has introduced a number of new terms, which he considers as more precise. It will be necessary, before we proceed farther, to insert his explanation of these terms.

"The expressions," says he, "which I have used Explanaare openings, shallows, ridges, nodules, corrugations, tion of his indentations, and pores.

Openings are those places where, by the accidental removal of the luminous clouds of the sun, its own solid body may be seen; and this not being lucid, the openings through which we see it may, by a common telescope, be mistaken for mere black spots, or their nuclei.

terms.

Bodies.

"Corrugations, I call that very particular and remarkable unevenness, ruggedness, or asperity, which is peculiar to the luminous solar clouds, and extends all over the surface of the globe of the sun. As the depressed parts of the corrugations are less luminous than the elevated ones, the disk of the sun has an appearance which may be called mottled.

Indentations are the depressed or low parts of the corrugations; they also extend over the whole surface of the luminous solar clouds.

Pores are very small holes or openings, about the middle of the indentations.

From the numerous observations of this philosopher he has drawn the following conclusions:

1. Openings are places where the luminous clouds of the sun are removed: large openings have generally shallows about them; but small openings are generally without shallows. They have generally ridges and nodules about them, and they have a tendency to run into each other. New openings often break out near other openings. Hence he supposes that the openings are occasioned by an elastic but not luminous gas, which comes up through the pores and incipient openings, and spreads itself on the luminous clouds, forcing them out of its way, and widening its passage. Openings sometimes differ in colour; they divide when decayed; sometimes they increase again; but when divided they usually decrease and vanish; sometimes they become large indentations, and sometimes they turn into

pores.

2. Shallows are depressed below the general surface of the sun, and are places from which the luminous solar clouds of the upper regions are removed. Their thickness is visible; sometimes they exist without openings in them. Incipient shallows come from the openings, or branch out from shallows already formed, and go forward. He supposes that the shallows are occasioned by something coming out of the openings, which, by its propelling motion, drives away the luminous clouds from the place where it meets with the least resistance; or which, by its nature, dissolves them as it comes up to them. If it be an elastic gas, its levity must be such as to make it ascend through the inferior region of the solar clouds, and diffuse itself among the superior luminous matter.

3. Ridges are elevations above the general surface of the luminous clouds of the sun. One of them, which he measured, extended over an angular space of 2′ 45"-9, which is nearly 75,000 miles.

Ridges generally accompany openings: but they often also exist in places where there are no openings. They usually disperse very soon. He supposes, that the openings permit a transparent elastic fluid to come out, which disturbs the luminous matter on the top, so as to occasion ridges and nodules; or, more precise ly, that some elastic gas, acting below the luminous clouds, lifts them up, or increases them; and at last forces itself a passage through them, by throwing them. aside.

4. Nodules are small, but highly elevated luminous VOL. III. Part I.

+

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6. The dark places of corrugations are indentations. Pores. Indentations are usually without openings, though in some places they contain small ones. They change to openings, and are of the same nature as shallows. They are low places, which often contain very small openings. They are of different sizes, and are extended all over the sun. With low magnifying powers they appear like points. The low places of indentations are pores. Pores increase sometimes, and become openings: they vanish quickly.

"It must be sufficiently evident," says Dr Herschel, "from what we have shown of the nature of openings, shallows, ridges, nodules, corrugations, indentations, and pores, that these phenomena could not appear, if the shining matter of the sun were a liquid; since, by the laws of hydrostatics, the openings, shallows, indentations, and pores, would instantly be filled up; nor could ridges and nodules preserve their elevation for a single moment. Whereas, many openings have been known to last for a whole revolution of the sun; and extensive elevations have remained supported for several days. Much less can it be an elastic fluid of an atmospheric nature: this would be still more ready to fill up the low places, and to expand itself to a level at the top. It remains, therefore, only for us to admit this shining matter to exist in the manner of empyreal, luminous, or phosphoric clouds, residing in the higher regions of the solar atmosphere."

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These observations are sufficient to prove, that the sun has an atmosphere of great density, and extending to a great height. Like our atmosphere, it is obviously subject to agitations, similar to our winds; and it is also transparent. The following is Dr Herschel's theoretical explanation of the solar pheno

mena.

Our

"We have admitted," says he, "that a transparent elastic gas comes up through the openings, by forcing itself a passage through the planetary clouds. observations seemed naturally to lead to this supposition, or rather to prove it; for, in tracing the shallows to their origin, it has been shown, that they always begin from the openings, and go forwards. We have also seen, that in one case, a particular bias given to incipient shallows, lengthened a number of them out in one certain direction, which evidently denoted a propelling force acting the same way in them all. I am, however, well prepared to distinguish between facts observed, and the cousequences that in reasoning upon them we may draw from them; and it will be easy to separate them, if that should hereafter be required.

If, however, it be now allowed, that the cause we have assigned may be the true one, it will then appear, that the operations which are carried on in the atmosphere of the sun are very simple and uniform.

"By the nature and construction of the sun, an elastic gas, which may be called empyreal, is constantly formed. This ascends everywhere, by a specific gravity less than that of the general solar atmospheric gas contained in the lower regions. When it goes up in moderate quantities, it makes itself small passages among the lower regions of clouds: these we have frequently observed, and have called them pores. We have shewn that they are liable to continual and quick changes, which must be a natural consequence of their fleeting generation.

"When this empyreal gas has reached the higher regions of the sun's atmosphere, it mixes with other gases, which, from their specific gravity, have their residence there, and occasions decompositions which produce the appearance of corrugations. It has been shown, that the elevated parts of the corrugations are small self-luminous nodules, or broken ridges; and I have used the name of self-luminous clouds, as a general expression for all phenomena of the sun, in what shape soever they may appear, that shine by their own light. These terms do not exactly convey the idea affixed to them; but those of meteors, coruscations, inflammations, luminous wisps, or others, which I might have selected, would have been liable to still greater objections. It is true, that when speaking of clouds, we generally conceive something too gross, and even too permanent, to permit us to apply that expression properly to luminous decompositions, which cannot float or swim in air, as we are used to see our planetary clouds do. But it should be remembered, that, on account of the great compression arising from the force of the gravity, all the elastic solar gases must be much condensed; and that, consequently, phenomena in the sun's atmosphere, which in ours would be mere transi

2

"The great light occasioned by the brilliant superior regions, must scatter itself on the tops of the inferior planetary clouds, and, on account of their great density, bring on a very vivid reflection. Between the interstices of the elevated parts of the corrugations, or self-luminous clouds, which, according to the observations that have been given, are not closely connected, the light reflected from the lower clouds will be plainly visible, and, being considerably less intense than the direct illumination from the upper regions, will occasion that faint appearance which we have called indentations.

"This mixture of the light reflected from the indentations, and that which is emitted directly from the higher parts of the corrugations, unless very attentively examined by a superior telescope, will only have the resemblance of a mottled surface.

"When a quantity of empyreal gas, more than what produces only pores in ascending, is formed, it will make itself small openings; or, meeting perhaps with some resistance in passing upwards, it may exert its action in the production of ridges and nodules.

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Lastly, If still further an uncommon quantity of this gas should be formed, it will burst through the planetary regions of clouds, and thus will produce great openings; then, spreading itself above them, it will occasion large shallows, and, mixing afterwards gradually with other superior gases, it will promote the increase, and assist in the maintenance, of the general luminous phenomena.

of the Heaven Bodies

Apparent Motious

of the

Heavenly Bodies.

orbit.

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SECT. I. Of the Apparent Motions of the Moon.

The moon, like the sun, has a peculiar motion from east to west. If we observe her any evening when she is situated very near any fixed star, we shall find her, in 24 hours, about 13° to the east of that star; and Monn's mo- her distance continually increases, till at last, after a tion in her certain number of days, she returns again to the same star from the west, having performed a complete revolution in the heavens. By a continued series of observations it has been ascertained, that the moon makes a complete revolution in 27.32166118036 days, or 27 days 7 hours 43' 11" 31" 35"". Such at least was the duration of its revolution at the commencement of 1700. But it does not remain always the same. From a comparison between the observations of the ancients and those of the moderns, it appears, that the mean motion of the moon in her orbit is accelerating. This acceleration, but just sensible at present, will gradually become more and more obvious. It is a point of great importance to discover, whether it will always continue to increase, or whether, after arriving at a certain maximum, it will again diminish. Observations could be of no service for many ages in the resolution of this question; but the Newtonian theory has enabled astronomers to ascertain that the acceleration is periodi cal.

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Elliptical.

81

Its eccentricity.

8%

The moon's motion in her orbit is still more unequal than that of the sun. In one part of her orbit she moves faster, in another slower. By knowing the time of a complete revolution, we can easily calculate the mean motion for a day, or any given time; and this mean motion is called the mean anomaly. The true motion is called the true anomaly: the difference between the two is called the equation. Now the moon's equation sometimes amounts to 6° 18′ 32".

Her apparent diameter varies with the velocity of her angular motion. When she moves fastest, her diameter is largest; it is smallest when her angular motion is slowest. When smallest, the apparent diameter is 0.489420°; when biggest, it is 0.558030°. Hence it follows, that the distance of the moon from the earth varies. By following the same mode of reasoning, which we have detailed in the last chapter, Kepler ascertained that the orbit of the moon is an ellipse, having the earth in one of its foci. Her radius vector describes equal areas in equal times; and her angular motion is inversely proportional to the square of her distance from the earth.

The eccentricity of the elliptic orbit of the moon, has been ascertained to amount to 0.0550368, (the mean distance of the earth being represented by unity); or the greater axis is to the smaller, nearly as 100,000 to 99,848.

That point of the moon's orbit which is nearest the earth, is called the perigee; the opposite point is the apogee. The line which joins these opposite points, is called the line of the moon's apsides. It moves slowly eastward, completing a sidereal revolution in 3232.46643 days, or nearly 9 years.

The inclination of the moon's orbit is also variable the greatest inequality is proportional to the cosine of twice the sun's angular distance from the ascending node, and amounts when a maximum to 0.14679°.

83

1. The greatest of all, and the one which was first as- The eveccertained, is called by astronomers the moon's evection, tion. It is proportional to the sine of twice the mean angular distance of the moon from the sun, minus the mean angular distance of the moon from the perigee of its orbit. Its maximum amounts to 1.3410°. In the oppositions and conjunctions of the sun and moon it coincides with the equation of the centre, which it always diminishes. Hence the ancients, who determined that equation by means of the eclipses, found that equation smaller than it is in reality.

84

2. There is another inequality in the motion of the Variations. moon, which disappears during the conjunctions and oppositions of the sun and moon; and likewise when these bodies are 90° distant from each other. It is at its maximum when their mutual distance is about 45°, and then amounts to about 0.594°. Hence it has been concluded to be proportional to the sine of twice the mean angular distance of the moon from the sun. inequality is called the variation. It disappears during the eclipses.

This

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3. The moon's motion is accelerated when that of Annual the sun is retarded, and the contrary. This occasions equation. an irregularity called the annual equation. It follows exactly the same law with that of the equation of the centre of the sun, only with a contrary sine. At its maximum it amounts to 0.18576°. During eclipses, it coincides with the equation of the sun.

86

The moon's orbit is inclined to the ecliptic at an angle of 6.14692°. The points where it intersects the ecliptic are called the nodes. Their position is not fixed in the heavens. They have a retrograde motion, that is to say, a motion contrary to that of the sun. This motion may be easily traced by marking the suc cessive stars which the moon passes when she crosses the ecliptic. They make a complete revolution of the Revolution heavens in 6793.3009 days. heavens in 6793.3009 days. The ascending node is of her. that in which the moon rises above the ecliptic towards nodes. the north pole, the descending node that in which she sinks below the equator towards the south pole. The motion of the nodes is subjected to several irregularities, the greatest of which is proportional to the sine of twice the angular distance of the sun from the ascending node of the lunar orbit. When at a maximum, it amounts to 1.62945°. The inclination of the orbit itself is variable. Its greatest inequality amounts to 0.14679°. It is proportional to the cosine of the same angle on which the irregularity in the motion of the nodes depends.

The apparent diameter of the moon varies as well as that of the sun, and in a more remarkable manner. When smallest, it measures 29.5'; when largest, 34'. This must be owing to the distance of the moon from the earth being subject to variations.

87

The great distance of the sun from the earth renders Moon's pait difficult to determine its parallax, on account of its rallax. minuteness. This is not the case with the moon. The distance of that luminary from the earth may be determined without much difficulty. E 2

Let