Secondaries of the equator are also called hour circles, because the arc of the equator, contained between any one of these circles and the meridian, shews the distance in time of that body from the meridian, the equator being divided into 24 hours.

8. The meridian also passes through the nadir (the lower pole of the horizon).

Secondaries of the horizon are called vertical circles. That vertical circle which intersects the meridian at right angles is called the prime vertical.

It will help the conception of the student to consider the meridian and other verticals of the horizon as remaining at rest, while the sphere revolves, carrying the equator and other circles.

The four points where the meridian and prime vertical intersect the horizon, are called the cardinal points. Those of the meridian, north and south; those of the prime vertical, east and west. The equator intersects the horizon in the east and west points (being poles of the meridian), and its inclination to the horizon equals the complement of the altitude of the celestial pole. The prime vertical also intersects the equator at the east and west points, and at an angle equal to the altitude of the pole.

The azimutha of a celestial object is measured by an arc of the horizon, intercepted between the meridian and a vertical circle passing through the object. In (Fig. 3) KO is the azimuth of the point S from the north.

The altitude of a celestial object, being its distance from the horizon measured on a secondary of the horizon, is greatest when the object is on the meridian.

9. The path of the Sun traced on the surface of the imaginary celestial sphere, among the fixed stars, is a great circle,

a The complement of the azimuth, or the arc intercepted between the prime vertical and the vertical through the object, is called the amplitude. Ed.

which he moves over, in a direction from west to east.

This

circle is called the ecliptic, because eclipses take place when the moon, at the new and full, is in or near this circle. The apparent motion of the sun, in this circle, is not entirely uniform; the motion being contrary to the diurnal motion, the interval between two meridian passages of the sun is greater than that of the fixed stars, and by four minutes nearly. This interval, between two passages of the sun over the meridian, is in its mean quantity called 24 hours, or a day. In 365 days, 6 hours and 9 minutes, the sun appears to complete the ecliptic. The seasons are connected with the positions of the sun in the ecliptic. The period, therefore, of his motion, called a year, becomes one of the most important divisions of time.

10. The moon completes her course among the fixed stars, by a motion from west to east, in 27 days 7 hours, returning nearly to the same place. Its apparent path is nearly a great circle, intersecting the ecliptic at an angle of about five degrees. Its motion also being contrary to the diurnal motion, the interval between its successive passages or transits over the meridian is greater than that of the fixed stars, and by 52 minutes, in its mean quantity. The moon is said to be in opposition to the sun, when near that part of the ecliptic opposite to the sun. The interval between two oppositions is nearly 30 days, and at each opposition the moon shines with a full phase. The use, in civil life, of this striking phenomenon, makes another important division of time, which is called a month.

11. The ecliptic necessarily intersects the equator, each being a great circle. The angle of intersection is nearly 23° 28'. The circumstance of the inclination, or obliquity of the ecliptic to the equator, explains the change of seasons. The true cause of the appearance of the obliquity of the ecliptic to the equator, will be afterwards shewn. If the ecliptic coincided with the equator, the sun would always rise and set in the east and west points, would always be at the same altitude when on

the meridian, and would be absent and present during equal spaces of time. Now the effect of the sun, with respect to heat, depends upon the time of his continuance above the horizon, and the greatest altitude to which he rises; therefore, if he moved in the equator, no alteration would take place, because these would be the same every day. But the ecliptic being inclined to the equator, when the sun is in that part which is between our visible pole and the equator, the greater part of each of the diurnal circles which he describes, is above our horizon, i.e. he is more than half the 24 hours above the horizon, and he passes the meridian between the equator and zenith. When southward of the equator, he is less than 12 hours above the horizon. When he is in the points of intersection of the ecliptic and equator, he is just 12 hours above the horizon, and it is then equal day and night. This latter circumstance takes place on the 20th of March and 23rd of September.

The sun is in that part of the ecliptic nearest our visible pole about the 21st of June, and then our days are longest, and in the part farthest from it on the 21st of December, when our days are shortest. The sun is about eight days longer on the northern side of the ecliptic than on the southern, and hence summer is eight days longer than winter. The greatest heat is not when the days are longest, but some time after, because the increase of heat during the day is greater than the decrease during the night, consequently heat must accumulate till the increments and decrements are equal; afterwards the decrease being greater than the increase, the heat will diminish. The same may be said with respect to cold.

12. The two parallels to the equator, or parallels of declination, touching the ecliptic, are called tropics or tropical circles, because when the sun is in these points of the ecliptic, he turns his course, as it were, back again toward the equator.

The points of the ecliptic of greatest declination, or the

tropical points, are called solstices, because the sun appears stationary, with respect to his approach to the poles.

13. A belt or zone extending on each side of the ecliptic about 8° is called the zodiac, from certain imaginary forms of animals conceived to be drawn in it, called signs of the zodiac. There are twelve signs, probably from there being twelve lunations during the course of the sun in the ecliptic. These are Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagitta. rius, Capricornus, Aquarius, and Pisces, and denoted by V, 8,

,,, me, 2, m, f, vs, w, X. The reason of distinguishing this space was, because the sun and planets were always observed within it. These figures served also to distinguish the position of the stars with respect to one another, and were therefore called the constellations of the zodiac. The space of the zodiac has always been noticed from the earliest records of astronomy. Some of the planets lately discovered are not confined to this space. One of them, Pallas, sometimes is distant above 62° from the ecliptic.

The first six constellations, beginning with Aries, were formerly on the northern side of the ecliptic, most probably when the description of the zodiac was first invented, and the six others on the southern. But by a comparison of observations made at a considerable interval from each other, it is found that the intersections of the ecliptic and equator move backward, in respect to the signs of the zodiac, the obliquity of the ecliptic remaining nearly the same. The equator moves on the ecliptic, the ecliptic continuing to pass nearly through the same stars. The intersections or the equinoctial points move backward at the rate of 1o in 71 years, and therefore, at present, the constellation Aries seems to be moved forward nearly 30° from the equinoctial point, yet astronomers still commence the twelve signs or divisions of the ecliptic at the equinoctial point, and name them after the constellations of the zodiac. This distinction ought to be attended to.

14. In the practice of astronomy, the most general and convenient method of ascertaining the position of any celestial object on the concave surface, is to determine its position with respect to the equator and vernal equinoctial point, that is, to determine its declination and right ascension. The right ascension of a celestial body is the arc of the equator intercepted, (reckoning according to the order of the signs), between the vernal equinoctial point, or the first point of Aries, and a secondary to the equator passing through the object. This is expressed both in time and space. Thus, if the arc intercepted be 15°, the right ascension may be said to be 15° or one hour, supposing the equator divided into twenty-four hours. The measure of twenty-four hours for the time of the diurnal revolution of the fixed stars, or the celestial sphere, is called sidereal time. Hence the interval in sidereal time between the passages of two fixed stars over the meridian, is the same as the difference of their right ascensions expressed in time.

The term, right ascension, originally had a reference to the rising of the celestial bodies. Now its use is much more circumscribed, but much more important, and therefore it might have been better to have adopted another term for expressing the arc intercepted between a secondary to the equator passing through the celestial object, and the first point of the equator.

15. The position of a celestial body, with respect to the equator, being ascertained, it is very often necessary to ascertain its position with respect to the ecliptic, i. e. to determine its longitude and latitude. This is done by spherical trigonometry.a

The longitude of a celestial object is measured by an arc of the ecliptic, intercepted between the first point of Aries

a Vide Appendix, Prop. IV.