of which in this section we see only the fronts, or risers, so that they appear merely as lines (showing the edge of each step) drawn one over the other.  At H on the plan, Fig. 21, we again see them represented as a series of lines, but here we are looking down on the top of them, and see only the upper surfaces, or “treads,” the edges again appearing as a series of lines.  At H on the longitudinal section, we see the same steps in section, and consequently their actual slope, which, however, could have been calculated from Figs. 18 and 21, by putting the heights shown in section with the width shown in plan.  The plan, Fig. 21, shows the thickness and position on the floor of the pillars, G G. Their height is shown in the sections.  The plan of a building is merely a horizontal section, cutting off the top, and looking down on the sectional top of the walls, so as to see all their thicknesses.  I have drawn (Fig. 24) a perspective sketch of one end of the plan (Fig. 22) of the building, on the same principle as was done with the section (Fig. 23), in order to show more intelligibly exactly what it is that a plan represents—­the building with the upper part lifted off.

Returning for a moment to the subject of the relation between the plan and the exterior design, it should be noted that the plan of a building being practically the first consideration, and the basis of the whole design, the latter should be in accordance with the principle of disposition of the plan.  For example, if we have an elevation (shown in diagram) showing two wings of similar design on either side of a center, designed so as to convey the idea of a grand gallery, with a suite of apartments on either side of similar importance—­if the one side only of the plan contains such a suite, and the opposite side is in reality divided up into small and inferior rooms, filled in as well as may be behind the architectural design—­the whole design is in that case only a blind or screen, giving a false exterior symmetry to a building which is not so planned.  This is an extreme case (or might be called so if it were not actually of pretty frequent occurrence); but it illustrates in a broad sense a principle which must be carried out in all cases, if the architecture is to be a real expression of the facts of the building.

In this lecture, which is concerned with general principles, a word may fittingly be said as to the subject of proportion, concerning which there are many misapprehensions.  The word may be, and is, used in two senses, first in regard to the general idea suggested in the words “a well proportioned building.”  This expression, often vaguely used, seems to signify a building in which the balance of parts is such as to produce an agreeable impression of completeness and repose.  There is a curious kind of popular fallacy in regard to this subject, illustrated in the remark which used to be often made about St. Peter’s, that it is so well proportioned