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CHAPTER II.

TERMINOLOGY AND ELEMENTARY GEOMETRICAL CONCEPTIONS AND

RELATIONS. TERMINOLOGY RELATING TO THE GLOBE OF THE

EARTH TO THE CELESTIAL SPHERE.—CELESTIAL PERSPECTIVE.

(81.) Several of the terms in use among astronomers have been explained in the preceding chapter, and others used anticipatively. But the technical language of every subject requires to be formally stated, both for consistency of usage and definiteness of conception. We shall therefore proceed, in the first place, to define a number of terms in perpetual use, having relation to the globe of the earth and the celestial sphere.

(82.) Definition 1. The axis of the earth is that diameter about which it revolves, with a uniform motion, from west to east; performing one revolution in the interval which elapses between any star leaving a certain point in the heavens, and returning to the same point again.

(83.) Def. 2. The poles of the earth are the points where its axis meets its surface. The North Pole is that nearest to Europe; the South Pole that most remote from it

(84.) Def. 3. The earth's equator is a great circle on its surface, equidistant from its poles, dividing it into two hemispheres—a northern and a southern; in the midst of which are situated the respective poles of the earth of those names. The plane of the equator is, therefore, a plane perpendicular to the earth's axis, and passing through its centre.

(85.) Def. 4. The terrestrial meridian of a station on the earth's surface, is a great circle of the globe passing through both poles and through the place. The plane of the meridian is the plane in which that circle lies.

(86.) Def. 5. The sensible and the rational horizon of any station have been already defined in art. 74.

(87.) Def. 6. A meridian line is the line of intersection of the plane of the meridian of any station with the plane of the sensible horizon, and therefore marks the north and south points of the horizon, or the directions in which a spectator must set out if he would travel directly towards the north or south pole.

(88.) Def. 7. The latitude of a place on the earth's surface is its angular distance from the equator, measured on its own terrestrial meridian: it is reckoned in degrees, minutes, and seconds, from 0 up to 90°, and northwards or southwards according to the hemisphere the place lies in. Thus, the observatory at Greenwich is situated in 51° 28' 40" north latitude. This definition of latitude, it will be observed, is to be considered as only temporary. A more exact knowledge of the physical structure and figure of the earth, and a better acquaintance with the niceties of astronomy, will render some modification of its terms, or a different manner of considering it, necessary.

(89.) Def. 8. Parallels of latitude are small circles on the earth's surface parallel to the equator. Every point in such a circle has the same latitude. Thus, Greenwich is said to be situated in the parallel of 51° 28' 40".

(90.) Def. 9. The longitude of a place on the earth's surface is the inclination of its meridian to that of some fixed station referred to as a point to reckon from. English astronomers and geographers use the observatory at Greenwich for this station; foreigners, the principal observatories of their respective nations. Some geographers have adopted the island of Ferro. Hereafter, when we speak of longitude, we reckon from Greenwich. The longitude of a place is, therefore, measured by the arc of the equator intercepted between the meridian of the place and that of Greenwich; or, which is the same thing, by the spherical angle at the pole included between these meridians.

(91.) As latitude is reckoned north or south, so longitude is usually said to be reckoned west or east. It would add greatly, however, to systematic regularity, and tend much to avoid confusion and ambiguity in computations, were this mode of expression abandoned, and longitudes reckoned invariably westward from their origin round the whole circle from 0 to 360°. Thus, the longitude of Paris is, in common parlance, either 2° 2C 22" east, or 357° 39' 38" west of Greenwich. But, in the sense in which we shall henceforth use and recommend others to use the term, the latter is its proper designation. Longitude is also reckoned in time at the rate of 24 h. for 360°, or 15° per hour. In this system the longitude of Paris is 23 h. 50 m. 38£s.*

(92.) Knowing the longitude and latitude of a place, it may be laid down on an artificial globe; and thus a map of the earth may be constructed. Maps of particular countries are detached portions of this general map, extended into planes; or, rather, they are representations on planes of such portions, executed according to certain conventional systems of rules, called projections, the object of which is either to distort as little as possible the outlines of countries from what they are on the globe—or to establish easy means of ascertaining, by inspection or graphical measurement, the latitudes and longitudes of places which occur in them, without referring to the globe or to books—or for other peculiar uses. See Chap. IV.

(93.) Def. 10. The Tropics are two parallels of latitude, one on the north and the other on the south side of the equator, over every point of which respectively, the sun in its diurnal course passes vertically on the 21st of March and the 21st of September in every year. Their latitudes are about 23° 28' respectively, north and south.

(94.) Def. 11. The Arctic and Antarctic circles are two small circles or parallels of latitude as distant from the north and south poles as the tropics are from the equator, that is to say, about 23° 28'; their latitudes, therefore, are about 66° 32'. We say about, for the places of these circles and of the tropics are continually shifting on the earth's surface, though with extreme slowness, as will be explained in its proper place.

* To distinguish minutes and seconds of time from those of angular measure wc sliall invariably adhere to the distinct system of notation here adopted (° ' ", and h. m. s.). Great confusion sometimes arises from the practice of using the same marks for both.

(95.) Def. 12. The sphere of the heavens or of the stars is an imaginary spherical surface of infinite radius, having the eye of any spectator for its centre, and which may be conceived as a ground on which the stars, planets, &c, the visible contents of the universe, are seen projected as in a vast picture. *

(96.) Def. 13. The poles of the celestial sphere are the points of that imaginary sphere towards which the earth's axis is directed.

(97.) Def. 14. The celestial equator, or, as it is often called by astronomers, the equinoctial, is a great circle of the celestial sphere, marked out by the indefinite extension of the plane of the terrestrial equator.

(98.) Def. 15. The celestial horizon of any place is a great circle of the sphere marked out by the indefinite extension of the plane of any spectator's sensible or (which comes to the same thing as will presently be shown), his rational horizon, as in the case of the equator.

(99.) Def. 16. The zenith and nadir\ of a spectator are the two points of the sphere of the heavens, vertically over his head, and vertically under his feet, or the poles of the celestial horizon; that is to say, points 90° distant from every point in it.

* The ideal sphere without us, to which we refer the places of objects, and which we carry along with us wherever wc go, is no doubt intimately connected by association, if not entirely dependent on that obscure perception of sensation in the retinas of our eyes, of which, even when closed and unexcited, wc cannot entirely divest them. We have a real spherical surface within our eyes, the seat of sensation and vision, corresponding, point for point, to the external sphere. On this the stars, &c. are really mapped down, as we have supposed them in the text to be, on the imaginary concave of the heavens. When the whole surface of the retina is excited by light, habit leads us to associate it with the idea of a real surface existing without us. Thus we become impressed with the notion of a thy and a heaven, but the concave surface of the retina itself is the true seat of all visible angular dimension and angular motion. The substitution of the retina for the heavens would be awkward and inconvenient in language, but it may always be mentally made. (Sec Schiller's pretty enigma on the eye in his Turandot)

f From Arabic words. Nadir corresponds evidently to the German nieiler (down), whence our nether.

(100.) Def. 17. Vertical circles of the sphere are great circles passing through the zenith and nadir, or great circles perpendicular to the horizon. On these are measured the altitudes of objects above the horizon—the complements to which are their zenith distances.

(101.) Def. 18. The celestial meridian of a spectator is the great circle marked out on the sphere by the prolongation of the plane of his terrestrial meridian. If the earth be supposed at rest, this is a fixed circle, and all the stars are carried across it in their diurnal courses from east to west. If the stars rest and the earth rotate, the spectator's meridian, like his horizon (art. 52.), sweeps daily across the stars from west to east. Whenever in future we speak of the meridian of a spectator or observer, we intend the celestial meridian, which being a circle passing through the poles of the heavens and the zenith of the observer, is necessarily a vertical circle, and passes through the north and south points of the horizon.

• (102.) Def. 19. The prime vertical is a vertical circle perpendicular to the meridian, and which therefore passes through the east and west points of the horizon.

(103.) Def. 20. Azimuth is the angular distance of a celestial object from the north or south point of the horizon (according as it is the north or south pole which is elevated), when the object is referred to the horizon by a vertical circle; or it is the angle comprised between two vertical planes—one passing through the elevated pole, the other through the object. Azimuth may be reckoned eastwards or westwards, from the north or south point, and is usually so reckoned only to 180° either way. But to avoid confusion, and to preserve continuity of interpretation when algebraic symbols are used (a point of essential importance, hitherto too little insisted on), we shall always reckon azimuth from the points of the horizon most remote from the elevated pole, westward (so as to agree in general directions with the apparent diurnal motion of the stars), and carry its reckoning from 0° to 360° if

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