zenith. Through E, draw HE O, at right angles to EZ; then HEO will represent the horizon (for the horizon is always at right angles to the zenith). Let EQ represent the plane of the equator, and at right angles to it, from the center of the earth, must be the earth's aris; therefore, EP, at right angles to EQ, is the direction of the pole. Or, by transposition, the arc POZQ; that is, the altitude of the pole is equal to the latitude of the place; which was to be demonstrated. In the same manner, we may demonstrate that the arc HQ is equal to the arc Z P; that is, the polar distance of the zenith is equal to the meridian altitude of the celestial equator. Now, we perceive, that by knowing the latitude, we know the several divisions of the celestial meridian, from the northern to the southern horizon, namely, O P, PZ, Z Q, and QH. (38.) We are now prepared to observe and determine the declinations of the stars. The declination of a star, or any celestial object, is its meridian distance from the celestial equator. This corresponds with latitude on the earth, and declination might have been called latitude. The term latitude, as applied in astronomy, is to be defined hereafter. Declina tion defined. 4 CHAP. III. To determine the declination of a star, we must observe How to its meridian altitude (by some instrument, say the mural find the de- circle, Fig. 2), and correct the altitude for refraction (see table of refraction); the difference will be the star's true altitude. clination of a star. Examples thod pursued If the true meridian altitude of the star is less than the meridian altitude of the celestial equator, then the declination of the star is south. If the meridian altitude of the star is greater than the meridian altitude of the equator, then the declination of the star is north. These truths will be apparent by merely inspecting Fig. 4. EXAMPLES. 1. Suppose an observer in the latitude of 40° 12′ 18′′ of the me- north, observes the meridian altitude of a star, from the to find any southern horizon, to be 31° 36′ 37′′; what is the declination star's decli- of that star? nation. From Take the latitude, 90° 0' 00" 40 12 18 Diff. is the meridian alt. of the equator, 49° 47′ 42′′ Alt. of star, 31° 36′ 37′′ 2. The same observer finds the meridian altitude of another star, from the southern horizon, to be 79° 31′ 42′′; what is the declination of that star? 3. The same observer, and from the same place, finds the meridian altitude of a star, from the northern horizon, to bo 51° 29' 53"; what is the declination of that star? 11 16 49 78° 43′ 11′′ Star from the pole (or polar dist. ), In this way the declination of every star in the visible heavens can be determined. Elements (39.) In Art. 28 we have explained how to obtain the for a chart difference of the right ascensions of the stars; and in the last of the stars. article we have shown how to obtain their declinations. With the declinations and differences of right ascensions, we may mark down the positions of all the stars on a globe or sphere the true representation of the appearance of the heavens. Quite a region of stars exists around the south pole, which are never seen from these northern latitudes; and to observe them, and define their positions, Dr. Halley, Sir John Herschel, and several other English and French astronomers, have, at different periods, visited the southern hemisphere. Thus, by the accumulated labors of the many astronomers, we at length have correct catalogues of all the stars in both hemispheres, even down to many that are never seen by the naked eye. The zero meridian of (40.) In Art. 28, we have explained how to find the differences of the right ascensions of the stars; but we have not right ascen yet found the absolute right ascension of any star, for the want sion. of the first meridian, or zero line, from which to reckon. But astronomers have agreed to take that meridian for the zero meridian, which passes through the sun's center the instant the sun comes to the celestial equator, in the spring (which point on the equator is called the equinoctial point); but the difficulty is to find exactly where (near what stars) this meridian line is. Before we can define this line, we must take observations on the sun, and determine where it crosses the equator, and from the time we can determine the place. But before we can place much reliance on solar observations, we must ask ourselves this question. Has the sun any parallax? CHAP. III. that is, is the position of the sun just where it appears to be? Is it really in the plane of the equator, when it appears to be there? Parallax. To all northern observers, is not the sun thrown back on the face of the sky, to a more southern position than the one it really occupies? Undoubtedly it is; and this change of position, caused by the locality of the observer, is called parallax; but, in respect to the sun, it is too small to be considered in these primary observations. The early astronomers asked themselves these questions, and based their conclusions on the following consideration: If the sun is materially projected out of its true place; if it is rallax insen- thrown to the southward, as seen by a northern observer, it mon observa- will cross the equator in the spring sooner than it appears Sun's pa sible, in com tions. Northern observations to cross. But let an observer be in the southern hemisphere, and, to him, the sun would be apparently thrown over to the north, and it would appear to cross the equator before it really did cross. Hence, if the sun is thrown out of place by parallax, an observer in the southern hemisphere would decide that the sun crossed the equator quicker, in absolute time, than that which would correspond to northern observations. But, in bringing observations to the test, it was found that and southern both northern and southern observers fixed on the same, or very nearly the same, absolute time for the sun crossing the equator. This proves that the position of the sun was not sensibly affected by parallax. compared. We will now suppose (for the sake of simplicity) that a sidereal clock has been so regulated as to run to the rate of sidereal time; that is, measure 24 hours between any two successive transits of the same star, over the same meridian, but the sidereal time not known. Also, suppose that, at the Observatory of Greenwich, in the year 1846, the following observations were made:* *In early times, such observations were often made. We took these results from the Nautical Almanac, and called them observations; but, for the purpose of showing principles, it is immaterial whether observations are real or imaginary. From these observations, it is required to determine the sidereal time, or the error of the clock; the time that the sun crossed the equator; the sun's right ascension; its longitude, and the obliquity of the ecliptic. It is understood that the observations for declinations must have been meridian observations, and, of course, must have been made at the instant of apparent noon, local solar time. By merely inspecting these observations, it will be perceived that the sun must have crossed the equator between the 20th and 21st; for at the apparent noon of the 20th, the declination was 11' 29".4 south; and on the 21st, at apparent noon, it was 12' 12' north. Between these two observations, the clock measured out 24 h. 3 m. 38.37 s., of sidereal time. If the sun had not changed its meridian among the stars, the time would have been just 24 hours. The excess (3 m. 38.37 s.) must be changed into arc, at the rate of four minutes to one degree. proportion: Hence, to find the arc, we have this As 4m : 3m. 38.37s. :: 1o : to the required result. The result is 54′ 35′′.4; the extent of arc which the sun changed right ascension during the interval between noon and noon of the 20th and 21st of March. To examine this matter understandingly, draw a line EQ (Fig. 5), and make it equal to 54′ 35′′.4. Computa. the equinox. From E, draw ES at right angles to EQ, and make it equal to 11' 29".4. From Q, draw QN at right angles to tions to find EQ, and make it equal to 12' 12". Then S will represent the sun at apparent noon, March 20th, and N the position of the sun at apparent noon on the 21st, and SN is the line of |