the division of the population having been ascertained, how shall we lay out the roads so as to make the different lines of communication, particularly the most frequented ones, as short as possible? Four plans ordinarily present themselves under which the ground selected for our city to be built on may be laid out: the square, hexagonal, octagonal, and circular. Of these, the hexagonal type seems, according to our mathematical calculations, the one which gives the greatest length of streets and the greatest amount of habitable surface, with the smallest consumption of space. As a rule, for cities the population of which is homogeneous, the octagonal and hexagonal plans are much preferable to the square in respect both to the utilization of the surface and the facility of communications. Unfortunately, both plans are liable to the objection that they give house-lots having acute angles of sixty degrees in the hexagonal, and of forty-five degrees in the octagonal plan. Practically the population finds it convenient to bear toward the center of the city, and, the more it bears that way, the more it is to its interest to do so. Consequently, the density of the population diminishes from the center toward the circumference. Under such conditions, the circular plan is very satisfactory. It has in effect the double advantage of furnishing direct roads to the center of the town, and of accommodating itself to giving to the houses in the outlying quarters the greater amount of space they require. For the center of cities, where the population is compact and homogeneous, where land is dear and communication is needed in every direction alike, the hexagonal plan, with the reservation of a few places for public monuments, is most convenient. This central part might be surrounded by a boulevard, beyond which the circular type might be adopted with modifications so as to avoid curved streets. The principal streets of each suburb might be directed toward the center of the city, and each suburb might in itself be laid out more or less according to the rectangular type. The transverse streets would, however, spread farther apart as the distance from the center became greater; and main diagonal streets might be arranged to cross the whole city, with few or only slight deviations. Beyond the suburbs, the principal radial streets might be continued for a considerable distance farther, but the transverse streets would nearly disappear. The accompanying design has been drawn according to these principles. It is worthy of remark that the sketch is more like the European cities that have grown up by progressive additions than the American cities which have been built on a so-called rational plan.
So far we have considered the question from an exclusively geometrical point of view. We may continue our study by referring to the influences which geographical, meteorological, commercial, and political conditions have had in the laying out of cities. Certain directions in the ways of communication are often imposed by the topographical situation; as, for example, when the town is crossed by a river or a
