to imps of a limited extent, more especially if they are maps of the polar regions of the globe. In this nue the meridians will be straight lines radiating from the centre, and the inrallels of latitude concentric circles, wham distances from the centre will respectively be equal to the cotangents of their latitudes.
In the other Mies of this projection, where the perspective plane is parallel to the horizon, or to any meridian, the construction is rendered troublesome on account of the parallels of latitude becoming curves of difficult delineation : these cases therefore are seldom brought into use.
Orthographic l'rojection.—la this projection the eye is supposed to be at an infinite distance, so that the visual rays leave the sphere in ler:11101 lines. The I lermpective plane on which a hendsphere is sup posed to be delineated Is the plane of that diameter which is perpen dicular to the visual rays : hens every point of the hemisphere is transferred to this plane by 1 erpeisliculars let fall upon it. It will be immediately seen from the figure, that the representation will decrease If E be the eye, and A, 0, c the hemisphere to be represented, a, a' C, n will be the plane of projection ; and the position on this plane of any point of the spherical surface will be indicated by a line drawn from that point through the plane to the eye. Thus the points K, as, c on the sphere will be transferred to the plane at Z', 1, or, a.
The advantages offered by this method of projection have brought it more into use than the methods before mentioned. It is especially calculated for maps of the world, as usually made in two hemispheres, from the circumstance of the representation being less distorted, and also on account of the meridians and parallels intersecting each other at right angles, as they do on the globe. Its construction also is less difficult than others, since all the great circles of the sphere are either circles or straight lines in the projection. The meridian of 20° W. is the one usually selected by English for the plane of projection in these maps of the world, because this meridian passes very nearly between the eastern and western continents, which there fore occupy their respective hemispheres.
Globular Projcction.—Thia projection, which is a modification of the Stereographic, was invented by the astronomer Do Lahire, who supposed the eye to be placed at a distance from the sphere equal to the sine of 45' ; that is, if the diameter of the sphere be equal to 200, the distance of the eye _from the nearest point of the circumference would be Some further modification was subsequently deemed desirable, in order that the meridians might intersect the equator at equal distances. This condition is very nearly fulfilled when the
distance of the eye is 50k, the diameter being 200 as before.
This projection is also much used in maps, of the world, but to simplify their construction, the meridians and parallels are projected into circular instead of elliptical arcs, the deviation from the strict law of the projection being too slight to affect the practical utility of the map.
Of Projection by Development.
The developments to be mentioned are two—the Conical and Cylindrical.
Conical Projection.—In this projection the sphere is supposed to be circumscribed by a cone, which touches the sphere at the circle intended to represent the middle parallel of the map. If the points on the sphere be now projected on the cone by lines drawn from the centre, it is clear that in a zone extending but a short distance on each side the middle parallel, as the zone a a' b b', the points on the cone would very nearly coincide in position with the corresponding points on the sphere. All the delineations having been thus made, the cone is then conceived to be unrolled, or developed on a plane surface.
Should the map be made to extend much above or below the middle parallel, the distant parts will be very much distorted. To remedy the defects of this projection, various modifications have been suggested, among which those of Flamsteed are generally held in the highest estimation. [Co sic PROJECTION.] Cylindrical Projection.—From what has been said of the cone, it will be easily understood that a cylinder may be applied to the sphere in a similar manner, and that a zone of very limited extent in latitude may, without very material error, be developed on a cylinder. The peculiarity of this method is, that the meridians, as well as the latitude circles, are projected in parallel straight lines ; a condition of the map which makes it very applicable to nautical purposes, and on which (partly) is founded the very ingenious method called Mercator's Pro jection, which is now so universally adopted in our charts, and which, in conclusion, we will briefly describe.