It was headed: "RECENT PROGRESS IN THE HIGHER MATHEMATICS." He crossed the title out carefully, and wrote above it: "AN EXAMINATION OF SOME SUPPOSED MATHEMATICAL IMPOSSIBILITIES." "There," he murmured, as he put the sheet back; "I think that such a theme, adequately treated, will considerably astonish my learned friends in general, and my esteemed critic, Van Huysman, in particular." From which remark it will be gathered that Franklin Marmion had certainly recrossed the dividing line between the two Planes of Existence..