The difficulties facing the teacher of plane geometry grow constantly more baffling. Enforced attendance at school until the boy or girl is sixteen, with a group of pupils often unfitted mentally, by environment, or by ambition for a high school education, presents an immediate and ever-looming problem. An insufficient number of trade schools or excessive ambition on the part of generous parents, desirous of seeing their children in the professions rather than in the trades, fills the classes of such a subject as plane geometry. Moreover the subject is generally required for college entrance, and is regarded almost universally as cultural, broadening, and conducive to mental development characterized by clear expression and logical thinking. The position of the teacher of this subject fifteen or twenty years ago when a select few with real ability pursued the subject was not nearly so complex. Now every youth who has managed to pass to the tenth grade and takes up plane geometry all but assumes that a passing understanding of the subject is his birthright. Perhaps it would be conceded that plane geometry is the first great obstacle to the youth's securing a coveted diploma. Or possibly it might be stated thus: it is in his attack upon this subject in which the frailty of his mental make-up is most in evidence, most pitilessly laid bare, if there is such weakness; or, on the other hand, his power of intellect is here first appreciated by others, and, with great satisfaction, by himself. Hence the instructor of plane geometry to-day who would teach the subject in a forceful and effective manner, developing his pupils, convincing them of its influence, its use and keen intellectual enjoyment, must be forever on his toes inventing and contriving devices and stratagems to teach satisfactorily this large group, less clever, less ambitious, less able, than heretofore, taken in the cross-section. What a wonderful people the citizens of the United States would be intellectually several generations hence if all who attempt a high school education really had the ambition and ability to master it.