the ecliptic, and meets the advancing sun somewhat before the whole sidereal circuit is completed. The annual retreat of the equinox is 50"-1, and this arc is described by the sun in the ecliptic in 20m 19.9. By so much shorter, then, is the periodical return of our seasons than the true sidereal revolution of the earth round the sun. As the latter period, or sidereal year, is equal to 365d 6h 9m 95.6, it follows, then, that the former must be only 365d 5h 48m 49.7; and this is what is meant by the tropical year.

*

(384.) We have already mentioned that the longer axis of the ellipse described by the earth has a slow motion of 11.8 per annum in advance. From this it results, that when the earth, setting out from the perihelion, has completed one sidereal period, the perihelion will have moved forward by 11"-8, which are must be described by the earth before it can again reach the perihelion. In so doing, it occupies 4m 39.7, and this must therefore be added to the sidereal period, to give the interval between two consecutive returns to the perihelion. This interval, then, is 365d 6h 13m 49-3, and is what is called the anomalistic year. All these periods have their uses in astronomy; but that in which mankind. in general are most interested is the tropical year, on which the return of the seasons depends, and which we thus perceive to be a compound phenomenon, depending chiefly and directly on the annual revolution of the earth round the sun, but subordinately also, and indirectly, on its rotation round its own axis, which is what occasions the precession of the equinoxes; thus affording an instructive example of the way in which a motion, once admitted in any part of our system, may be traced in its influence on others with which at first sight it could not possibly be supposed to have any thing to do.

(385.) As a rough consideration of the appearance of the earth points out the general roundness of its form, and more exact inquiry has led us first to the discovery of its elliptic figure, and, in the further progress of refinement, to the perception of minuter local deviations from that figure; so, in investigating the solar motions, the first notion we obtain is that of an orbit, generally speaking, round, and not far from a circle, which, on more careful

• These numbers, as well as all the other numerical data of our system, are taken from Mr. Baily's Astronomical Tables and Formula, unless the contrary is expressed.

and exact examination, proves to be an ellipse of small excentricity, and described in conformity with certain laws as above stated. Still minuter inquiry, however, detects yet smaller deviations again from this form and from these laws, of which we have a specimen in the slow motion of the axis of the orbit spoken of in art. 372; and which are generally comprehended under the name of perturbations and secular inequalities. Of these deviations, and their causes, we shall speak hereafter at length. It is the triumph of physical astronomy to have rendered a complete account of them all, and to have left nothing unexplained, either in the motions of the sun or in those of any other of the bodies of our system. But the nature of this explanation cannot be understood till we have developed the law of gravitation, and carried it into its more direct consequences. This will be the object of our three following chapters; in which we shall take advantage of the proximity of the moon, and its immediate connection with and dependence on the earth, to render it, as it were, a stepping-stone to the general explanation of the planetary movements. We shall conclude this by describing what is known of the physical constitution of the

sun.

(386). When viewed through powerful telescopes, provided with coloured glasses, to take off the heat, which would otherwise injure our eyes, the sun is observed to have frequently large and perfectly black spots upon it, surrounded with a kind of border, less completely dark, called a penumbra. Some of these are represented at a, b, c, d, in Plate I. fig. 2, at the end of this volume. They are, however, not permanent. When watched from day to day, or even from hour to hour, they appear to enlarge or contract, to change their forms, and at length to disappear altogether, or to break out anew in parts of the surface where none were before. In such cases of disappearance, the central dark spot always contracts into a point, and vanishes before the border. Occasionally they break up, or divide into two or more, and in those cases offer every evidence of that extreme mobility which belongs only to the fluid state, and of that excessively violent agitation which seems only compatible with the atmospheric or gaseous state of matter. The scale on which their movements take place is immense. single second of angular measure, as seen from the earth, corresponds on the sun's disc to 461 miles; and a circle of this

A

diameter (containing therefore nearly 167000 square miles) is the least space which can be distinctly discerned on the sun as a visible area. Spots have been observed, however, whose linear diameter has been upwards of 45000 miles; and even, if some records are to be trusted, of very much greater extent. That such a spot should close up in six weeks' time (for they seldom last much longer), its borders must approach at the rate of more than 1000 miles a day.

(387.) Many other circumstances tend to corroborate this view of the subject. The part of the sun's disc not occupied by spots is far from uniformly bright. Its ground is finely mottled with an appearance of minute, dark dots, or pores, which, when attentively watched, are found to be in a constant state of change. There is nothing which represents so faithfully this appearance as the slow subsidence of some flocculent chemical precipitates in a transparent fluid, when viewed perpendicularly from above: so faithfully, indeed, that it is hardly possible not to be impressed with the idea of a luminous medium intermixed, but not confounded, with a transparent and non-luminous atmosphere, either floating as clouds. in our air, or pervading it in vast sheets and columns like flame, or the streamers of our northern lights, directed in lines perpendicular to the surface.

(388.) Lastly, in the neighbourhood of great spots, or extensive groups of them, large spaces of the surface are often observed. to be covered with strongly marked curved or branching streaks, more luminous than the rest, called faculæ, and among these, if not already existing, spots frequently break out. They may, perhaps, be regarded with most probability, as the ridges of immense waves in the luminous regions of the sun's atmosphere, indicative of violent agitation in their neighbourhood. They are most commonly, and best seen, towards the borders of the visible disc, and their appearance is as represented in Plate I. fig. 1. (389.) But what are the spots? Many fanciful notions have been broached on this subject, but only one seems to have any degree of physical probability, viz. that they are the dark, or at least comparatively dark, solid body of the sun itself, laid bare to our view by those immense fluctuations in the luminous regions of

* Mayer, Obs. Mar. 15, 1758. "Ingens macula in sole conspiciebatur, cujus diameter diam. solis."

20

its atmosphere, to which it appears to be subject. Respecting the manner in which this disclosure takes place, different ideas again have been advocated. Lalande (art. 3240,) suggests, that emiFig. 55.

nences in the nature of mountains are actually laid bare, and project above the luminous ocean, appearing black above it, while their shoaling declivities produce the penumbræ, where the luminous fluid is less deep. A fatal objection to this theory is the uniform shade of the penumbra and its sharp termination, both inwards, where it joins the spot, and out

wards, where it borders on the bright surface. A more probable view has been taken by Sir William Herschel, who considers the luminous strata of the atmosphere to be sustained far above the level of the solid body by a transparent elastic medium, carrying on its upper surface (or rather, to avoid the former objection, at some considerably lower level within its depth) a cloudy stratum. which, being strongly illuminated from above, reflects a considerable portion of the light to our eyes, and forms a penumbra, while the solid body shaded by the clouds, reflects none. (See fig.) The temporary removal of both the strata, but more of the upper than the lower, he supposes effected by powerful upward currents of the atmosphere, arising, perhaps, from spiracles in the body, or from local agitations.

(390.) When the spots are attentively watched, their situation on the disc of the sun is observed to change. They advance regularly towards its western limb or border, where they disappear, and are replaced by others which enter at the eastern limb, and which, pursuing their respective courses, in their turn disappear at the western. The apparent rapidity of this movement is not uniform, as it would be were the spots dark bodies passing, by an independent motion of their own, between the earth and the sun; but is swiftest in the middle of their paths across the disc, and very slow at its borders. This is precisely what would be the case supposing them to appertain to and make part of the visible surface

*Phil. Trans. 1801.

of the sun's globe, and to be carried round by a uniform rotation of that globe on its axis, so that each spot should describe a circle parallel to the sun's equator, rendered elliptic by the effect of perspective. Their apparent paths also across the disc conform to this view of their nature, being, generally speaking, ellipses, much elongated, concentric with the sun's disc, each having one of its chords for its longer axis, and all these axes parallel to each other. At two periods of the year only do the spots appear to describe straight lines, viz., on and near to the 11th of June and the 12th of December, on which days, therefore, the plane of the circle, which a spot situated on the sun's equator describes (and consequently, the plane of that equator itself), passes through the earth. Hence it is obvious, that the plane of the sun's equator is inclined to that of the ecliptic, and intersects it in a line which passes through the place of the earth on these days. The situation of this line, or the line of the nodes of the sun's equator as it is called, is, therefore, defined by the longitudes of the earth as seen from the sun at those epochs, which are respectively 80° 21' and 260° 21' (=80° 21'+180°) being, of course, diametrically opposite in direction.

(391.) The inclination of the sun's axis (that of the plane of its equator) to the ecliptic is determined by ascertaining the proportion of the longer and the shorter diameter of the apparent ellipse, described by any remarkable, well-defined spot; in order to do which, its apparent place on the sun's disc must be very precisely ascertained by micrometric measures, repeated from day to day as long as it continues visible, (usually about 12 or 13 days, according to the magnitude of the spots, which always vanish by the effect of foreshortening before they attain the actual border of the disc-but the larger spots being traceable closer to the limb than the smaller.*) The reduction of such observations, or the conclusion from them of the element in question, is complicated with the effect of the earth's motion in the interval of the observations, and with its situation in the ecliptic, with respect to the line of nodes. For simplicity, we will suppose the earth situated as it is on the 10th of March, in a line at right angles to that of the nodes, i. e. in the heliocentric longitude 170° 21', and to remain there sta

* The great spot of December, 1719, is stated to have been seen as a notch in the limb of the sun.