The Nomograph as an Instrument in Map Making

Abstract

THE word is a convenient term to apply to graphical devices for plotting great-circle routes and distances on azimuthal, conical, and cylindrical map projections such as have recently been described in the Geographical Review.' The nomographs for cylindrical and azimuthal projections are their transverse and equatorial Variants respectively, thus they include the whole or parts of families of great circles joining two points on the sphere i800 apart. If a nomograph be superimposed over its corresponding map so that the center lines or center points coincide, the great-circle course between any two points on the map and the distance between the points can be interpolated by shifting the nomograph parallel to its center line in the case of cylindrical projections or by simple rotation in the case of azimuthal and conical projections. Examples of nomographs for four commonly used azimuthal projections are shown in Figure i. It is distressing how often great circles are incorrectly drawn on maps, and it would be well if this particular function of nomographs were used more often, especially by the great army of journalistic cartographers. The author has for some time past been using nomographs on the orthographic and azimuthal equidistant projections for this purpose. Their ease of operation and the precise results obtained are a constant delight to one who so often has to beribbon maps with great-circle routes. But the potentialities of nomographs for the actual construction of map projections seem to have been entirely unrealized up to the present. Yet they permit the construction of any oblique case of any azimuthal, conical, or cylindrical projection with great ease and accuracy and without any mathematical computation whatsoever. Some projections in their oblique form-notably the orthographic and the stereographic -can of course be constructed by other graphic methods,2 but the nomograph produces projections with surprising speed. The author drew an orthographic grid spaced at 200 and centered at 450 N. in 50 minutes. To illustrate the procedure, the construction of an orthographic projection tangent at 350 N. will be described. This is the procedure followed in making any azimuthal projection, with only minor and rather obvious differences. The circular nomograph is placed on a drawing board and covered with a rectangular piece of tracing paper that overlaps the nomograph on the sides but not at the top and bottom and is tacked to the board. A needle or round-shanked thumbtack is firmly thrust vertically through tracing paper and nomograph at the center of the latter. As the needle or tack remains in position until the new grid is completed, it is well first to reinforce the