In considering the nature of the textbook in geometry we need to bear in mind the fact that the subject is being taught to-day in America to a class of pupils that is not composed like the classes found in other countries or in earlier generations. In general, in other countries, geometry is not taught to mixed classes of boys and girls. Furthermore, it is generally taught to a more select group of pupils than in a country where the high school and college are so popular with people in all the walks of life. In America it is not alone the boy who is interested in education in general, or in mathematics in particular, who studies geometry, and who joins with others of like tastes in this pursuit, but it is often the boy and the girl who are not compelled to go out and work, and who fill the years of youth with a not over-strenuous school life. It is therefore clear that we cannot hold the interest of such pupils by the study of Euclid alone. Geometry must, for them, be less formal than it was half a century ago. We cannot expect to make our classes enthusiastic merely over a logical sequence of proved propositions. It becomes necessary to make the work more concrete, and to give a much larger number of simple exercises in order to create the interest that comes from independent work, from a feeling of conquest, and from a desire to do something original. If we would "cast a glamor over the multiplication table," as an admirer of Macaulay has said that the latter could do, we must have the facilities for so doing. It therefore becomes necessary in weighing the merits of a textbook to consider: (1) if the number of proved propositions is reduced to a safe minimum; (2) if there is reasonable opportunity to apply the theory, the actual applications coming best, however, from the teacher as an outside interest; (3) if there is an abundance of material in the way of simple exercises, since such material is not so readily given by the teacher as the seemingly local applications of the propositions to outdoor measurements; (4) if the book gives a reasonable amount of introductory work in the use of simple and inexpensive instruments, not at that time emphasizing the formal side of the subject; (5) if there is afforded some opportunity to see the recreative side of the subject, and to know a little of the story of geometry as it has developed from ancient to modern times.