The Homolo-parabolic Projection

This study aims at the construction of an equal-area projection which has less degree of distortion in the middle latitude areas including Japan and her neighbouring regions. As for the equal-area projection having parabolic curves as meridians, Lieut.-Col. J. E. E. Craster, a British cartographer had already referred to it in his article in "Geographical Journal" (1929). The present writer thoroughly cleared up its mathematical foundation and also calculated the distortion at every 10°of latitude and longitude. Furthermore, he compared it with that of the Sanson-Flamsteed projection and found out that the parabolic projection is better than the Sanson-Flamsteed in that the state of distortion in the middle latitudes is much more satisfactory in the former. In the next place, since it proved to be unsatisfactory to express the poles and their neighbouring areas on the map constructed by the parabolic projection, the writer used the Mollweide projection for drawing the high latitude areas as J. E. Goode, an American cartographer did in his homolosine projection. Two projections were connected each other at about 42°of latitude. The new projection thus made is called the "homolo-parabolic" projection by the writer. A world map drawn by this projection is shown in Fig. 11 at the end of this paper