asterism are known, many of the surrounding ones may easily be found, by means of alignments. For instance, the line formed by the three stars in the belt, if

Fig. 30.- Equatorial Constellations, visible in the south near the zenith, Oct. 23, at 10 P. M.

354. Fig. 29 represents in like manner the appearance of the heavens a little south of the zenith in May: the bright star Arcturus (a Boötis) being then nearly on the meridian. The constellation Hercules is easily recognised by means of the trapezium formed by four of its stars.

355. In Fig. 30 the square of Pegasus is a very marked object, and this once recognised in the sky, may, by means of star-maps, be made the start-point of many new alignments.

356. The first magnitude stars should be first known; then the second; and so on till the positions of all the brighter ones in the different constellations are impressed upon the memory—no difficult task after a little practice, and comparison of the sky itself with good small maps.

LESSON XXIX.-APPARENT MOTION OF THE SUN. DIFFERENCE IN LENGTH BETWEEN THE SIDEREAL AND SOLAR DAY. CELESTIAL LATITUDE AND LONGITUDE. THE SIGNS OF THE ZODIAC. SUN'S APPARENT PATH. HOW THE TIMES OF SUNRISE AND SUNSET, AND THE LENGTH OF THE DAY AND NIGHT, MAY BE DETERMINED BY MEANS OF THE CELESTIAL Globe.

357. The effect of the Earth's daily movement upon the Sun is precisely similar to its effect upon the stars; that is, the Sun appears to rise and set every day; but in consequence of the Earth's yearly motion round it, it appears to revolve round the Earth more slowly than the stars; and it is to this that we owe the difference between star-time and sun-time, or, in other words, between the lengths of the sidereal and solar day.

358. How this difference arises is shown in Fig. 31, in which are seen the Sun, and the Earth in two positions in its orbit, separated by the time of a complete rotation. In the first position of the Earth are shown one observer, a, with the Sun on his meridian, and another, b, with a star on his: the two observers being exactly on

arises.

opposite sides of the Earth, and in a line drawn through the centres of the Earth and Sun. In the second position, when the same star comes to 5's meridian, a sees the Sun still to the east of his, and he must be carried by the Earth's rotation to c before the Sun occupies the same apparent position in the heavens it formerly did that is, before the Sun is again in his meridian. The solar day, therefore, will be longer than the sidereal one by the time it takes a to travel this distance.

Of course, were the Earth at rest, this difference could not have arisen, and the solar day is a result of the Earth's

motion in its orbit, combined with its rotation.

359, Moreover, the Earth's motion in its orbit is not uniform, as we shall see subsequently; and, as a consequence, the apparent motion of the Sun is not uniform, and solar days are not of the same length; for it is evident that if the Earth sometimes travels faster, and therefore rther, in the interval of one rotation than it does at

others, the observer a has further to travel before he gets to c; and as the Earth's rotative movement is uniform, he requires more time. In a subsequent chapter it will be shown how this irregularity in the apparent motion of the Sun is obviated.

360. The apparent yearly motion of the Sun is so important that astronomers map out the celestial sphere by a second method, in order to indicate his motion more easily; for as the plane of the celestial equator, like the plane of the terrestrial equator, does not coincide with the plane of the ecliptic, the Sun's distance from the celestial equator varies every minute. To get over this difficulty, they make of the plane of the ecliptic a sort of second celestial equator. They apply the term celestial latitude to angular distances from it to the poles of the heavens, which are 90° from it north and south. They apply the term celestial longitude to the angular distancereckoned on the plane of the ecliptic-from the position occupied by the Sun at the vernal equinox, reckoning from left to right up to 360°. This latitude and longitude may be either heliocentric or geocentric, that is, reckoned from the centre either of the Sun or Earth respectively.

361. The celestial equator in this second arrangement is represented by a circle called the zodiac, which is not only divided, like all other circles, into degrees, &c., but into signs of 30° each. These, with their symbols, are as follow :

:

At the time these signs were adopted the Sun entered the constellation Aries at the vernal equinox, and occupied

in succession the constellations bearing the same names; but at present, owing to the precession of the equinoxes, which we shall explain subsequently, the signs no longer correspond with the constellations, which must therefore not be confounded with them.

362. Now it follows, that, as these two methods of dividing the celestial sphere, and of referring the places of the heavenly bodies to it, are built, as it were, one on the plane of the terrestrial equator, and the other on the plane of the ecliptic, (1) the angle formed by the celestial equator with the plane of the ecliptic is the same as that formed by the terrestrial one,—that is, 231° nearly; and (2) the poles of the heavens are each the same distance, -that is, 23, from the celestial poles.

Moreover, if we regard the centre of the celestial sphere as lying at the centre of the Earth, it is clear that the two planes will intersect each other at that point, and that half of the ecliptic will be north of the celestial equator and half below it; and there will be two points opposite to each other at which the ecliptic will cross the celestial equator.

363. Now as the Sun keeps to the ecliptic, it follows that at different parts of its path it will cross the celestial equator, be north of it, cross it again, and be south of it, and so on again; in other words, its latitude remaining the same, its declination or distance from the celestial equator will change.

364. Hence it is, that although the Sun rises and sets every day, its daily path is sometimes high, sometimes low. At the vernal equinox,—that is, when it occupies one of the points in which the zodiac cuts the equator,—it rises due east, and sets due west, like an equatorial star; then gradually increasing its north declination, its daily path approaches the zenith, and its rising and setting points advance northwards, until it occupies the part of