If the early "originals" are one-step exercises, and a pupil is required to recite rapidly, a habit of quick expression is easily acquired that leads to close attention on the part of all the class. Students as a rule recite slower than they need to, from mere habit. Phlegmatic as we think the German is, and nervous as is the American temperament, a student in geometry in a German school will usually recite more quickly and with more vigor than one with us. Our extensive blackboards have something to do with this, allowing so many pupils to be working at the board that a teacher cannot attend to them all. The result is a habit of wasting the minutes that can only be overcome by the teacher setting a definite but reasonable time limit, and holding the pupil responsible if the work is not done in the time specified. If this matter is taken in hand the first day, and special effort made in the early weeks of the year, much of the difficulty can be overcome. As to the nature of the recitation to be expected from the pupil, no definite rule can be laid down, since it varies so much with the work of the day. In general, however, a pupil should state the theorem quickly, state exactly what is given and what is to be proved, with respect to the figure, and then give the proof. At first it is desirable that he should give the authorities in full, and later give only the essential part in a few words. It is better to avoid the expression "by previous proposition," for it soon comes to be abused, and of course the learning of section numbers in a book is a barbarism. It is only by continually stating the propositions used that a pupil comes to have well fixed in his memory the basal theorems of geometry, and without these he cannot make progress in his subsequent mathematics. In general, it is better to allow a pupil to finish his proof before asking him any questions, the constant interruptions indulged in by some teachers being the cause of no little confusion and hesitancy on the part of pupils. Sometimes it is well to have a figure drawn differently from the one in the book, or lettered differently, so as to make sure that the pupil has not memorized the proof, but in general such devices are unnecessary, for a teacher can easily discover whether the proof is thoroughly understood, either by the manner of the pupil or by some slight questioning. A good textbook has the figures systematically lettered in some helpful way that is easily followed by the class that is listening to the recitation, and it is not advisable to abandon this for a random set of letters arranged in no proper order.