motion of the sun is presented to us under its least involved form, and is studied, from the station we occupy, to the greatest advantage. So that, independent of the importance of that luminary to us in other respects, it is by the investigation of the laws of its motions in the first instance that we must rise to a knowledge of those of all the other bodies of our system.

(256.) The ecliptic, which is its apparent path among the stars, is traversed by it in the period called the sidereal year, which consists of 365d 6h 9m 95.6, reckoned in mean solar time, or 366d 6h 9m 9s-6 reckoned in sidereal time. The reason of this difference (and it is this which constitutes the origin of the difference between solar and sidereal time) is, that as the sun's apparent annual motion among the stars is performed in a contrary direction to the apparent diurnal motion of both sun and stars, it comes to the same thing as if the diurnal motion of the sun were so much slower than that of the stars, or as if the sun lagged behind them in its daily course. Where this has gone on for a whole year, the sun will have fallen behind the stars by a whole circumference of the heavens or, in other words - in a year, the sun will have made fewer diurnal revolutions, by one, than the stars. So that the same interval of time which is measured by 366d 6h, &c. of sidereal time, if reckoned in mean solar days, hours, &c. will be called 365d 6h, &c. Thus, then, is the proportion between the mean solar and sidereal day esta.. blished, which, reduced into a decimal fraction, is that of 1.00273791 to 1. The measurement of time by these different standards may be compared to that of space by the standard feet, or ells of two different nations; the proportion of which, once settled, can never become a source of error.

(257.) The position of the ecliptic among the stars may, for our present purpose, be regarded as invariable. It is true that this is not strictly the case; and on comparing together its position at present with that which it held at the most distant epoch at which we possess

observations, we find evidences of a small change, which theory accounts for, and whose nature will be hereafter explained; but that change is so excessively slow, that for a great many successive years, or even for whole centuries, this circle may be regarded as holding the same position in the sidereal heavens.

(258.) The poles of the ecliptic, like those of any other great circle of the sphere, are opposite points on its surface, equidistant from the ecliptic in every direction. They are of course not coincident with those of the equinoctial, but removed from it by an angular interval equal to the inclination of the ecliptic to the equinoctial (23°28′), which is called the obliquity of the ecliptic. In the annexed figure, if Pp represent the north and south poles (by which, when used without qualification we always mean the poles of the equinoctial), and EQAV the equinoctial, V SA W the ecliptic, and Kk, its poles the spherical angle QVS is the obliquity of the ecliptic, and is equal in angular measure to P K or SQ. If we suppose the sun's apparent motion to be in the direction V S A W, V will be the vernal and A the autumnal equinox. S and W, the two points at which the ecliptic is most distant from the equinoctial, are termed solstices, because, when arrived there, the sun ceases to recede from the equator, and (in that sense, so far as its motion in declination is concerned) to stand still in the heavens. S, the point where the sun has the greatest northern declination, is called the summer solstice, and W, that where it is farthest south, the winter. These epithets obviously have their origin in the dependence of the seasons on the sun's declination, which will be explained in the next chapter. The circle EK PQkp, which passes through the poles of the ecliptic and equinoctial, is called the solstitial colure; and a meridian drawn through the equinoxes, PV p A, the equinoctial colure.

(259.) Since the ecliptic holds a determinate situation in the starry heavens, it may be employed, like the equinoctial, to refer the positions of the stars to, by circles

drawn through them from its poles, and therefore perpendicular to it. Such circles are termed, in astronomy, circles of latitude - the distance of a star from the ecliptic, reckoned on the circle of latitude passing through it, is called the latitude of the stars - and the arc of the ecliptic intercepted between the vernal equi nox and this circle, its longitude. In the figure X is a

star, PXR a circle of declination drawn through it, by which it is referred to the equinoctial, and K X T a circle of latitude referring it to the ecliptic — then, as VR is the right ascension, and R X the declination, of X, so also is V T its longitude, and T X its latitude. The use of the terms longitude and latitude, in this sense, seems to have originated in considering the ecliptic as forming a kind of natural equator to the heavens, as the terrestrial equator does to the earth the former holding an invariable position with respect to the stars, as the latter does with respect to stations on the earth's surface. The force of this observation will presently become apparent.

(260.) Knowing the right ascension and declination of an object, we may find its longitude and latitude, and vice versâ. This is a problem of great use in physical astronomy - the following is its solution: In our last figure, E K PQ, the solstitial colure is of

course 90° distant from V, the vernal equinox, which is one of its poles so that V R (the right ascension) being given, and also V E, the arc E R, and its measure, the spherical angle EP R, or K P X, is known. In the spherical triangle K P X, then, we have given, 1st, The side PK, which, being the distance of the poles of the ecliptic and equinoctial, is equal to the obliquity of the ecliptic; 2d, The side P X, the polar distance, or the complement of the declination RX; and, 3d, the included angle K PX; and therefore, by spherical trigonometry, it is easy to find the other side K X, and the remaining angles. Now K X is the complement of the required latitude X T, and the angle PKX being known, and P K V being a right angle (because S V is 90°), the angle X K V becomes known. Now this is no other than the measure of the longitude VT of the object. The inverse problem is resolved by the same triangle, and by a process exactly similar.

(261.) The same course of observations by which the path of the sun among the fixed stars' is traced, and the ecliptic marked out among them, determines, of course, the place of the equinox V upon the starry sphere, at that time a point of great importance in practical astronomy, as it is the origin or zero point of right ascension. Now, when this process is repeated at considerably distant intervals of time, a very remarkable phenomenon is observed; viz. that the equinox does not preserve a constant place among the stars, but shifts its position, travelling continually and regularly, although with extreme lowness, backwards, along the ecliptic, in the direction V W from east to west, or the contrary to that in which the sun appears to move in that circle. As the ecliptic and equinoctial are not very much inclined, this motion of the equinox from east to west along the former, conspires (speaking generally) with the diurnal motion, and carries it, with reference to that motion, continually in advance upon the stars: hence it has acquired the name of the precession of the equinoxes, because the place of the equinox among the stars, at

every subsequent moment, precedes (with reference to the diurnal motion) that which is held the moment before. The amount of this motion by which the equinox travels backward, or retrogrades (as it is called), on the ecliptic, is 0° 0' 50" 10 per annum, an extremely minute quantity, but which, by its continual accumulation from year to year, at last makes itself very palpable, and that in a way highly inconvenient to practical astronomers, by destroying, in the lapse of a moderate number of years, the arrangement of their catalogues of stars, and making it necessary to reconstruct them. Since the formation of the earliest catalogue on record, the place of the equinox has retrograded already about 30°. The period in which it performs a complete tour of the ecliptic, is 25,868 years.

(262.) The immediate uranographical effect of the precession of the equinoxes is to produce a uniform increase of longitude in all the heavenly bodies, whether fixed or erratic. For the vernal equinox being the initial point of longitudes, as well as of right ascension, a retreat of this point on the ecliptic tells upon the longitudes of all alike, whether at rest or in motion, and produces, so far as its amount extends, the appearance of a motion in longitude common to all, as if the whole heavens had a slow rotation round the poles of the ecliptic in the long period above mentioned, similar to what they have in twenty-four hours round those of the equinoctial.

(263.) To form a just idea of this curious astronomical phenomenon, however, we must abandon, for a time, the consideration of the ecliptic, as tending to produce confusion in our ideas; for this reason, that the stability of the ecliptic itself among the stars is (as already hinted, art. 257.) only approximate, and that in consequence its intersection with the equinoctial is liable to a certain amount of change, arising from its fluctuation, which mixes itself with what is due to the principal uranographical cause of the phenomenon. This cause will become at once apparent, if, instead of regarding