The object of the first conversation ( Math. Gazette , March 1928) was to suggest the advantages of using a definition of right angle different from that of Euclid for the study of “spaces” of which the dimensions can be distinguished from each other, a very common type of space. For brevity we will refer to this study as “Dimensional Geometry,” and call the right angles “dimensional right angles.” The second conversation is intended to suggest that “dimensional spaces” facilitate the study of Non-Euclidean Geometry.