PROJECTION. (From the Latin pro jicere, to throw forward). In its general sense, the term signifies the representation of the form of a given figure upon a given surface by means of a pencil of visual, light, or other rays in such a manner that the figure in the pro jection corresponds point by point to the given figure. For example, shadows are the pro jections of objects upon different surfaces which intercept the rays of light from any source, not already intercepted by the objects them selves. They represent the most elementary forms of plane projections, and while corre sponding in general outline to the objects pro jected, yet differ from them to a greater or lesser extent according to the distance of the object from the source of light, the distance of the plane of projection from the object, the angle between the plane of projection and the direction of the rays of light, the position of the observer's eye, etc.
In the mathematical construction of pro-. jections, however, instead of a single plane being used to intercept the projecting rays, another surface, such as one formed by two planes at right angles to each other, is taken and the various points of any object, plane or in space of three dimensions, projected to that surface from any point assumed as the center of the projection.
When the projection shows three dimensions of the object projected, it is commonly known as perspective, the mathematical theory of which together with the various classes of such pro jections employed in mechanics and for solving the problems of applied mathematics, will be found under the title PERSPECTIVE in this En cyclopedia. The present article is confined to the consideration of the various projections used in connection with geographical and geodetical work in general, and to their em ployment in the construction of maps for special purposes.
In general the word when used with reference to maps, has nothing whatever to do with geometrical projection from a point. It simply refers to a transformation of latitude and longitude on the spherical or spheroidal earth into planer magnitudes. A suitable in troduction to this particular phase of the sub is given under the title MAP in this Encyclopedia, wherein the three principal per spective projections of the sphere — the ortho graphic, the stereographic and the gnomonic, are clearly explained and illustrated. Of these,
the orthographic and the stereographic are rarely used at the present time except in the construction of what may be called pictorial maps; but, the gnomonic and several of its modifications are extensively used for the con struction of star charts in general, and espe cially for charts showing the apparent tracks of shooting stars on account of the facility in determining the radiant point, the great circles on the celestial sphere appearing as straight lines on the projection. For similar reasons it is used in the construction of sailing charts showing steamship routes, and is much more satisfactory for this purpose than Mercator's projection, which although almost universally used for nautical charts, is specially applicable for those used by sailing ships.
The chief value of the perspective projec tions lies in their adaptability for representing large areas of the earths surface. Usually, they represent a hemisphere; but, by the employ ment of the projection first proposed by Lahire in 1701 and subsequently modified by Lieut.
H. James of the Ordnance of Great Britain and Ireland, fully two-thirds of the sphere can be shown within the bounding circle. This is ac complished by assuming the eye above the sphere at a distance equal to half the radius and perpendicular over the center of i the plane of projection. The plane of projection is not that of a great circle, but is parallel to it and re moved from it nearer to the eye by 23 degrees.
A simple and easily constructed projection which can be effectively used in representing a hemisphere may be briefly described as follows: Draw a circle and bisect it by horizontal and vertical diameters; divide the circle into equal parts representing degrees of latitude; divide the vertical diameter into a corresponding num ber of equal parts; and divide the horizontal diameter into equal parts representing degrees of longitude. This will establish three points in every parallel of latitude, i.e., two in the cir cumference and one in the vertical diameter, through which the arc of a circle may be drawn representing the corresponding parallel of lati tude, and also three points in every meridian, i.e., one at each pole and one in the horizontal diameter or equator, through which the arc of a circle may be drawn representing a meridian.