The Distortions of Map Projections

Abstract

Briefly speaking, the distortions of map projection are presented in their scale alteration, area alteration, and angle alteration. The alterations of the orthodrome and loxodrome are derived from them. If we are going to study something on a large scale map, we are able to have a pretty exact concept of its pattern of arrengement and distribution. But if the scale is not a large one we may have an incorrect concept of them.Partaining to this aspect of cartography, not mach has been published so far. Therefore, I should like to introduce briefly the distortion theory. Since Tissot's indicatrix is the most fundamental one concerning the map distortion theory, I am going to explain it in more detail, and will treat some of the recent status of its practical application. For instance, Robinson's diagrams, Russian authors' monograms, etc.There are, I believe, many unsolved problems related to the map projections which will be eventually solved in near future. From the standpoint of the distortion theory, they mry be summarized as follows : 1. If the earth is taken asha sphere by the common method, some distortions is innevitable. But these distortions are very small. So, we may negect those distortions either on the very small scale maps of large area, or on the very large scale maps of small area. Therefore the probrem in question is most important for maps of intermedium scales which a certain degree of distortion is unavoidable.2. We are able to study precisely the distortions of large sc ale maps, except the conformal projections which have been studied more closely.3. We need to establish and study the concrete and useful method of map projections, and selection of a certain map projections of a certain purpose.4. It is necessary to establish a more concrete theory and systems of map projection from the scientifc point of view. So far, Goussinsky's classification of map projection is seemed to be the most appropriate one that has hither been used.