to the pupil with an air of reality, they serve a good purpose, but if made a part of textbook work, they soon come to have less interest than the exercises of a more abstract character. If a teacher can relate the problems in topographical drawing to the pupil's home town, and can occasionally set some outdoor work of the nature here suggested, the results are usually salutary; but if he reiterates only a half-dozen simple propositions time after time, with only slight changes in the nature of the application, then the results will not lead to a cultivation of power in geometry,—a point which the writers on applied geometry usually fail to recognize.
One of the simple applications of this book relates to the rounding of corners in laying out streets in some of our modern towns where there is a desire to depart from the conventional square corner. It is also used in laying out park walks and drives.
The figure in the middle of the page represents two streets, AP and BQ, that would, if prolonged, intersect at C. It is required to construct an arc so that they shall begin to curve at P and Q, where CP = CQ, and hence the "center of curvature" O must be found.
The problem is a common one in railroad work, only here AP is usually oblique to BQ if they are produced to meet at C, as in the second figure on [page 218]. It is required to construct an arc so that the tracks shall begin to curve at P and Q, where CP = CQ.
The problem becomes a little more complicated, and correspondingly more interesting, when we have to find the center of curvature for a street railway track that must turn a corner in such a way as to allow, say, exactly 5 feet from the point P, on account of a sidewalk.
