two plumb-lines be regarded as mathematically parallel. They converge towards the centre of the earth: but for very small intervals (as in the area of a building - in one and the same town, &c.) the difference from exact parallelism is so small, that it may be practically disregarded. An interval of a mile corresponds to a convergence of plumb-lines amounting to about 1 minute. The zenith and nadir are the poles of the celestial horizon; that is to say, points 90° distant from every point in it. The celestial horizon itself is the vanishing line of a system of planes parallel to the sensible and rational horizon.

(81.) DEF. 5. 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.

(82.) DEF. 6. The poles of the heavens are the points of the sphere to which the earth's axis is directed; or the vanishing points of all lines parallel thereto.

(83.) DEF. 7. 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. The celestial equator is a great circle of the heavens, marked out by the indefinite extension of the plane of the terrestrial, and is the vanishing line of all planes parallel to it. This circle is called by astronomers the equinoctial.

(84.) DEF. 8. The terrestrial meridian of a station on the earth's surface is a great circle passing through both the poles and through the place. When its plane is prolonged to the sphere of the heavens, it marks out the celestial meridian of a spectator stationed at that place. When we speak of the meridian of a

spectator, we intend the celestial meridian, which is a vertical circle passing through the poles of the heavens.

The plane of the meridian is the plane of this circle, and its intersection with the sensible horizon of the spectator is called a meridian line, and marks the north and south points of his horizon.

(85.) DEF. 9. 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. The altitude and azimuth of an object being known, therefore, its place in the visible heavens is determined. For their simultaneous measurement, a peculiar instrument has been imagined, called an altitude and azimuth instrument, which will be described in the next chapter.

(86.) DEF. 10. 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. (87.) DEF. 11. 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′′.

(88.) DEF. 12. 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.

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° 20′ 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 23h. 50m. 384s.

(89.) 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. III.

(90.) A globe, or general map of the heavens, as well as charts of particular parts, may also be constructed,

and the stars laid down in their proper situations relative to each other, and to the poles of the heavens and the celestial equator. Such a representation, once made, will exhibit a true appearance of the stars as they present themselves in succession to every spectator on the surface, or as they may be conceived to be seen at once by one at the centre of the globe. It is, therefore, independent of all geographical localities. There will occur in such a representation neither zenith, nadir, nor horizon-neither east nor west points; and although great circles may be drawn on it from pole to pole, corresponding to terrestrial meridians, they can no longer, in this point of view, be regarded as the celestial meridians of fixed points on the earth's surface, since, in the course of one diurnal revolution, every point in it passes beneath each of them. It is on account of this change of conception, and with a view to establish a complete distinction between the two branches of Geography and Uranography, that astronomers have adopted different terms (viz. declination, and right ascension) to represent those arcs in the heavens which correspond to latitudes and longitudes on the earth. It is for this reason that they term the equator of the heavens the equinoctial; that what are meridians on the earth are called hour circles in the heavens, and the angles they include between them at the poles are called hour angles. All this is convenient and intelligible; and had they been content with this nomenclature, no confusion could ever have arisen. Unluckily, the early astronomers have employed also the words latitude and longitude in their uranography, in speaking of arcs of circles not corresponding to those meant by the same words on the earth, but having reference to the motion of the sun and planets among the stars. It is now too late to remedy this confusion, which is ingrafted into every existing work on astronomy: we can only regret, and warn the reader of it, that he may be on his guard when, at a more advanced period of our work, we shall have occasion to *T, the earth; ygape, to describe or represent: ougars, the heavens,

define and use the terms in their celestial sense, at the same time urgently recommending to future writers the adoption of others in their places.

(91.) As terrestrial longitudes reckon from an assumed fixed meridian, or from a determinate point on the equator; so right ascensions in the heavens require some determinate hour circle, or some known point in the equinoctial, as the commencement of their reckoning, or their zero point. The hour circle passing through some remarkably bright star might have been chosen; but there would have been no particular advantage in this; and astronomers have adopted, in preference, a point in the equinoctial, called the equinox. through which they suppose the hour circle to pass, from which all others are reckoned, and which point is itself the zero point of all right ascensions, counted on the equinoctial.

The right ascensions of celestial objects are always reckoned eastward from the equinox, and are estimated either in degrees, minutes, and seconds, as in the case of terrestrial longitudes, from 0° to 360°, which completes the circle; or, in time, in hours, minutes, and seconds, from Oh. to 24h. The apparent diurnal motion of the heavens being contrary to the real motion of the earth, this is in conformity with the westward reckoning of longitudes. (Art 87.)

(92.) Sidereal time is reckoned by the diurnal motion of the stars, or rather of that point in the equinoctial from which right ascensions are reckoned. This point may be considered as a star, though no star is, in fact, there; and, moreover, the point itself is liable to a certain slow variation, -so slow, however, as not to affect, perceptibly, the interval of any two of its successive returns to the meridian. This interval is called a sidereal day, and is divided into 24 sidereal hours, and these again into minutes and seconds. A clock which marks sidereal time, i. e. which goes uniformly at such a rate as always to show Oh. Om. Os. when the equinox comes on the meridian, is called a