which began the study in September of the past school year and continued it till February, afford some suggestion of

Fig. 6. the scope of inventional geometry. Each pupil is equipped with a ruler, which he uses merely as a straight-edge, a pair of drawing-compasses, and a right-line pen. For a short period I drawings are made with lead-pencil, till the pupil has acquired a little manual skill; then the change is made to pen, and all problems must be drawn in ink. Neatness and accuracy are insisted upon, and secured.

The class, having worked at their desks the problems assigned for a lesson, come up for recitation, and are directed to put their