A PROPOSAL OF THE NEW NETHOD FOR AN INTERRUPTED MAP PROJECTION OF THE WORLD

Abstract

Although a considerable number of improvements have been made for the interrupted projections of normal type for f he past fifty years, the author believes that these attempts have been unsuccessful due to the discordance of function and beauty. In consequence of examining defects of these improved projections, the author has found a new-type interrupted world map projection and would like to present it in this paper. Designing the interrupted world map projection, there are two problems to overcoms first. One is how many segments should be interrupted and other is what kind of shape is more convenient use. The more the world maps is interrupted, the less distortion of each continent or segment on the map is and the less intercontinental relationship should appear, and vice versa. Therefore, it is not desirable that world map projections are interrupted into too many or too few segments. For the practical use, it is more convenient that each continent is contained in a segment. On the other hand, the shape is generally asymmetrical in this case. From the aesthetical point of view, however, it is more desirable that the shape is symmetrical. In this case, it is rather difficult to select the central meridian, since a continent should not be separated into two or more segments. In order to obtain a more desirable interrupted map projection of the world, it is essential that some improvements should be done for these two problems, and that the shape should be determined prior to the number of interruption, because the number of segments is easily determined by the shape. Examining symmetrical interrupted projectins having been presented, the author has found that all of these projections are designed to be lateral symmetrization, and considered that an interrupted world map projection with point-symmetrization would be desirable to the autor's intension. The interrupting method proposed by author is as follows : 1) The northern hemisphere is divided into two segments in the proportion of 2 : 1 so that Eurasia and North America are included in each segment. (The Central Meridian of both segments are 75°E and 105°W). 2) The southern hemisphere is divided into two segments in the proportion of 1 : 2 so that Australasia and South America-Africa are comprised in each segment. (The Central Meridian of both segments are 135°E and 45°W). The new method mentioned above is designated as the symmetrical interrupting method, because it is designed with lateral symmetry in each segment and pointsymmetry on the whole. This method will be able to apply to many “conventional projections.” After examining Sinusoidal, Mollweide, Homolosine and several truncated projections, the author is convinced that the Mollweide is most suitable for this method due to the fact that it reduced the degree of distortion of the continents more effectively. The interrupted projection of the world based on the Mollweide by using is new method is presented in Fig. 10.