taught by going over demonstrative geometry, then taking up mechanical drawing, and adding to these personal experience. The author has secured all this and much more. He appeals first to the inventive faculty, seeks expression through the hand, and brings before the eye accurate and beautiful forms of the pupil's own constructing. The eye is trained to accuracy and similarity of forms, invention is quickened, comparison and judgment are constantly exercised, and inductive growth of mind is directly promoted. Besides the manual skill gained in constructing figures, and the power acquired to deal with original questions
through the constant appeal to invention, the pupil gains by his own efforts proofs of theorems really conclusive in themselves, though not the syllogistic form of proof belonging to the deductive science.
In but one of a great number of schools visited has the writer found inventional geometry used, and in that school quite out of the design of the author. It should precede demonstrative geometry, so as to give the pupil many concepts to draw upon when he takes up syllogistic demonstration. Demonstrative geometry then becomes an easier subject, and he is surer of what he is doing, because he has more general notions as a basis. In the school alluded