This is shown on Fig. 19, where the portion showing the roof is also marked N, and it will be seen that the surface which is sloping in Fig. 17 is seen in the side elevation only as a space between a top and bottom line. We see the length of the roof here, and its height, but for its slope we go to the end elevation. Neither elevation tells us, however, what is inside the building; but the section (Fig. 18) shows us that it has an arched ceiling, and two stories, a lower and a higher one. The section is the building cut in half, showing the end of the walls, the height and depth of the window openings, the thickness of the floor, etc., and as all parts which are opposite the eye are shown in the drawing, the inside of the cross wall at the end of the building is shown as a part of the section drawing, between the sectional walls. In Fig. 23 the section is sketched in perspective, to show more clearly what it means. Another section is made lengthwise of the building (Fig. 20). It is customary to indicate on the plan by dotted lines the portion through which the section is supposed to be made. Thus on the plans the lines A B and C D are drawn, and the corresponding sections are labeled with the same lines.

As with the elevation, one section must be compared with another to get the full information from them. Thus in Fig. 18, the ceiling, M, is shown as a semicircle; in Fig. 20, it is only a space between the top and bottom lines. It is, certainly, shaded here to give the effect of rotundity, but that is quite a superfluity. On Fig. 18 the height of the side windows is shown at F, and the thickness of the wall in which they are made. In Fig. 20 (F) their width and spacing are shown. In Fig. 18 some lines drawn across, one over the other, are shown at H. These are the stairs, 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 that you are not aware of its great size, etc. - a criticism which has been slain over and over again, but continues to come to life again. The fact that this building does not show its size is true. But the inference drawn is the very reverse of the truth. One object in architectural design is to give full value to the size of a building, even to magnify its apparent size; and St. Peter's does not show its size, because it is ill proportioned, being merely like a smaller building, with all its parts magnified. Hence the deception to the eye, which sees details which it is accustomed to see on a smaller scale, and underrates their actual size, which is only to be ascertained by deliberate investigation. This confusion as to scale is a weakness inherent in the classical forms of columnar architecture, in which the scale of all the parts is always in the same proportion to each other and to the total size of the building so that a large Doric temple is in most respects only a small one magnified. In Gothic architecture the scale is the human figure, and a larger building is treated, not by magnifying its parts, but by multiplying them. Had this procedure been adopted in the case of St. Peter's, instead of merely treating it with a columnar order of vast size, with all its details magnified in proportion, we should not have the fault to find with it that it does not produce the effect of its real size. In another sense, the word "proportion" in architecture refers to the system of designing buildings on some definite geometrical system of regulating the sizes of the different parts.