Book II offers two general lines of application that may be introduced to advantage, preferably as additions to the textbook work. One of these has reference to topographical drawing and related subjects, and the other to geometric design. As long as these can be introduced 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. [Illustration] 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. [Illustration] 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_. [Illustration] 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. [Illustration] The problem becomes still more difficult if we have two roads of different widths that we wish to join on a curve. Here the two centers of curvature are not the same, and the one road narrows to the other on the curve. The solutions will be understood from a study of the figures. The number of problems of this kind that can easily be made is limitless, and it is well to avoid the danger of hobby riding on this or any similar topic. Therefore a single one will suffice to close this group. [Illustration]