the equator, intercepted between the vernal equinox and that secondary to the equator which passes through the star. Declination is the distance of a body from the equator measured on a secondary to the latter. Therefore, right ascension and declination correspond to terrestrial longitude and latitude,-right ascension being reckoned from the equinoctial colure, in the same manner as longitude is reckoned from the meridian of Greenwich. On the other hand, celestial longitude and latitude are referred, not to the equator, but to the ecliptic. Celestial longitude is the distance of a body from the vernal equinox measured on the ecliptic. Celestial latitude is the distance from the ecliptic measured on a secondary to the latter. Or, more briefly, longitude is distance on the ecliptic: latitude, distance from the ecliptic. The north polar distance of a star is the complement of its declination.

Parallels of latitude are small circles parallel to the equator. They constantly diminish in size, as we go from the equator to the pole. The tropics are the parallels of latitude which pass through the solstices. The northern tropic is called the tropic of Cancer; the southern, the tropic of Capricorn. The polar circles are the parallels of latitude that pass through the poles of the ecliptic, at the distance of twenty-three and a half degrees from the poles of the earth.

The elevation of the pole of the heavens above the horizon of any place is always equal to the latitude of the place. Thus, in forty degrees of north latitude we see the north star forty degrees above the northern horizon; whereas, if we should travel southward, its elevation would grow less and less, until we reached the equator, where it would appear in the horizon. Or, if we should travel northwards, the north star would rise continually higher and higher, until, if we could reach the pole of the earth, that star would appear directly over head. The elevation of the equator above the horizon of any place is equal to the complement of the latitude. Thus, at the latitude of forty degrees

north, the equator is elevated fifty degrees above the southern horizon.

The earth is divided into five zones. That portion of the earth which lies between the tropics is called the torrid zone; that between the tropics and the polar circles, the temperate zones; and that between the polar circles and the poles, the frigid zones.

The zodiac is the part of the celestial sphere which lies about eight degrees on each side of the ecliptic. This portion of the heavens is thus marked off by itself, because all the planets move within it.

After endeavoring to form, from the definitions, as clear an idea as we can of the various circles of the sphere, we may next resort to an artificial globe, and see how they are severally represented there. I do not advise to begin learning the definitions from the globe ; the mind is more improved, and a power of conceiving clearly how things are in Nature is more effectually acquired, by referring every thing, at first, to the grand sphere of Nature itself, and afterwards resorting to artificial representations to aid our conceptions. We can get but a very imperfect idea of a man from a profile cut in paper, unless we know the original. If we are acquainted with the individual, the profile will assist us to recall his appearance more distinctly than we can do without it. In like manner, orreries, globes, and other artificial aids, will be found very useful, in assisting us to form distinct conceptions of the relations existing between the different circles of the sphere, and of the arrangements of the heavenly bodies; but, unless we have already acquired some correct ideas of these things, by contemplating them as they are in Nature, artificial globes, and especially orreries, will be apt to mislead us.

I trust you will be able to obtain the use of a globe,*

*A small pair of globes, that will answer every purpose require by the readers of these Letters, may be had of the publishers of this Work, at a price not exceeding ten dollars; or half that sum for a celestial globe, which will serve alone for studying astronomy.

L. A

way

to aid you in the study of the foregoing definitions, or doctrine of the sphere; but if not, I would recommend the following easy device. To represent the earth, select a large apple, (a melon, when in season, will be found still better.) The eye and the stem of the apple will indicate the position of the two poles of the earth. Applying the thumb and finger of the left hand to the poles, and holding the apple so that the poles may be in a north and south line, turn this globe from west to east, and its motion will correspond to the diurnal movement of the earth. Pass a wire or a knitting needle through the poles, and it will represent the axis of the sphere. A circle cut around the apple, half between the poles, will be the equator; and several other circles cut between the equator and the poles, parallel to the equator, will represent parallels of latitude; of which, two, drawn twenty-three and a half degrees from the equator, will be the tropics, and two others, at the same distance from the poles, will be the polar circles. A great circle cut through the poles, in a north and south direction, will form the meridian, and several other great circles drawn through the poles, and of course perpendicularly to the equator, will be secondaries to the equator, constituting meridians, or hour circles. A great circle cut through the centre of the earth, from one tropic to the other, would represen the plane of the ecliptic; and consequently a line cut round the apple where such a section meets the surface, will be the terrestrial ecliptic. The points where this circle meets the tropics indicate the position of the solstices; and its intersection with the equator, that of the equinoctial points.

The horizon is best represented by a circular piece of pasteboard, cut so as to fit closely to the apple, be ing movable upon it. When this horizon passed through the poles, it becomes the horizon of the equa tor; when it is so placed as to coincide with he earth's equator, it becomes the horizon of the poles; and in every other situation it represents the horizon of a

place on the globe ninety degrees every way from it. Suppose we are in latitude forty degrees; then let us place our movable paper parallel to our own horizon, and elevate the pole forty degrees above it, as near as we can judge by the eye. If we cut a circle around the apple, passing through its highest part, and through the east and west points, it will represent the prime vertical.

Simple as the foregoing device is, if you will take the trouble to construct one for yourself, it will lead you to more correct views of the doctrine of the sphere, than you would be apt to obtain from the most expensive artificial globes, although there are many other useful purposes which such globes serve, for which the apple would be inadequate. When you have thus made a sphere for yourself, or, with an artificial globe before you, if you have access to one, proceed to point out on it the various arcs of azimuth and altitude, right ascension and declination, terrestrial and celestial latitude and longitude,-these last being referred to the equator on the earth, and to the ecliptic in the heavens.

When the circles of the sphere are well learned, we may advantageously employ projections of them in various illustrations. By the projection of the sphere is meant a representation of all its parts on a plane. The plane itself is called the plane of projection. Let us take any circular ring, as a wire bent into a circle, and hold it in different positions before the eye. If we hold it parallel to the face, with the whole breadth opposite to the eye, we see it as an entire circle. If we turn it a little sideways, it appears oval, or as an ellipse; and, as we continue to turn it more and more round, the ellipse grows narrower and narrower, until, when the edge is presented to the eye, we see nothing but a line. Now imagine the ring to be near a perpendicular wall, and the eye to be removed at such a distance from. it, as not to distinguish any interval between the ring and the wall; then the several figures under which the ring is seen will appear to be inscribed on the wall, and we

shall see the ring as a circle, when perpendicular to a straight line joining the centre of the ring and the eye, or as an ellipse, when oblique to this line, or as a straight line, when its edge is towards us.

It is in this manner that the circles of the sphere are projected, as represented in the following diagram, Fig. 2.

Here, various circles are represented as projected on the meridian, which is supposed to be situated directly before the eye, at some distance from it. The horizon

HO, being perpendicular to the meridian, is seen edgewise, and consequently is projected into a straight line. The same is the

case with the prime vertical Z N, with the equator E Q, and the several small circles parallel to the equator, which represent the two tropics and the two polar circles. In fact, all circles whatsoever, which are perpendicular to the plane of projection, will be represented by straight lines. But every circle which is perpendicular to the horizon, except the prime vertical, being seen obliquely, as Z M N, will be projected into an ellipse, one half only of which is seen, the other half being on the other side of the plane of projection. In the same manner, P R P, an hour circle, is represented by an ellipse on the plane of projection.