It may be seen at once that such a treatment of arches differs from the arrangement necessary to make plain lintels effective. The pillars on the front of Greek temples were indeed slightly farther apart at the middle entrance, and the centre was moreover further accented by the point of the pediment. But on the sides the rows of from thirteen to sixteen columns had equal interspace and no noticeably heavier columns or embankment of any kind at the ends, for none was necessary. The series appeared ended whenever it stopped, and did not carry the attention over, nor demand some finish to "hold it down," as does the arch. The pillars, to be sure, completely surrounded the temple, and so were, in name, continuous. But on a building with square corners, the other sides do not carry the series on to the eye (with variations in foreshortening of the ends) as in a circular structure, and the effect of continuity is not immediate.

Many examples might be given of buildings with pillars and lintels on the façade, which have no visible modifications of central or end columns to give balance or symmetry to the whole, and yet which are perfectly satisfactory as repeated series and do not demand either such treatment or further continuation, but are complete and finished: London, Trafalgar Square; Rome, Pantheon; Vienna, St. Karl, Barrome Kirche; Berlin, Schillerplatz, etc. These have the centre accented by the superstructure, but there is no discernible modification of the series itself.

Examples might be multiplied, but there are sufficient to illustrate the essential stability of repeated vertical units and to contract them with the outward-tending, run-on effect of arches which need various kinds of treatments to finish a series. kinds of treatments to finish a series.

Of one hundred and sixty-five examples of such series examined, only seven do not conform to the principles we have considered, and these are proportionately unsatisfactory. Forty-five illustrate buildings where the arches go completely around the outside of a structure, so that the series instead of requiring an end simply runs into itself again. It will be noticed further, that unlike series of columns around rectangular Greek temples, these are around circular structures where the series does not change its direction suddenly but by degrees. With the exception of courts and cloisters where the observer stands within and sees the whole series, these are all around domes, baptisteries, etc., where the end arches in the field at any one point of view are seen in perspective gradually fading off and yet leading attention on around the building. There may indeed be arches which go across square-cornered buildings or even around them, but in these cases some other device is necessary to make each side a finished series in itself. The mere fact of its continuance around a corner where it cannot be seen from the same point of view is not enough. (These various arrangements of arches on a flat façade will be taken up later.) Rows of arches are often used around towers square as well as round, but towers from their very shape and size allow the observer to see different sides from nearly the same point of view, so the series is not broken up into sections on different sides of the tower as it is in a larger building. Twenty more examples are of arches in interiors and are all of arches down a nave, with either a regular arch or an arch motif carried across the apse. It might be supposed that an arrangement of arches in an interior would be more difficult than on an exterior surface, since the genius of an arch is its outward thrust and its tendency to run on. Without careful treatment it would spoil the interior by trying to overstep its bounds; by making certain walls look wider than others; the arched sections utterly discrete in general character from the plain or otherwise decorated section. In point of fact, the use of the arch-series in interiors is quite conventionalized, and all the illustrations are of loggias, or of churches where the arch goes down the nave and in a more or less modified form across the apse. In the Sistine Chapel the arched windows go down the side walls and across the end in a vaulted double-arch. In some cases a series of Roman arches down the nave has a more or less pointed arch across the apse, but in every case the continuity has been kept in some way so that the series is unbroken. Moreover the columns in the cathedral naves are often so high and the arches so proportionally narrow that the pillar instead of the arch is taken as the unit. This is somewhat true in St. Mark, Venice, also in St. Sophia, Constantinople, where the large arches are divided into sections of seven smaller ones, each one of which is so narrow that the pillar is felt as the repeated unit instead of the arch; or if the arch be taken, the narrow span prevents it from too great outward thrust.

Thirty of the arch-series are on façades of buildings or in structures by themselves, as gates and triumphal arches, where the central arch is larger than the other, thereby emphasizing the middle point and drawing attention to it away from the ends. This centralizing a series or balancing it as a whole may be accomplished in various ways. Two examples make the central arch larger instead of smaller. Six make the end arches smaller while four make them larger. It will be readily seen that just which one of these variations is chosen for the series depends on the function of the series. The central arch is wider, with only one exception, when the series is of arched doors and the central door is the main entrance; while the end arches are more apt to be varied when the series is purely decorative and serves no function. The central balance may be further gained by differences of level. In the decorations of many façades, especially the early Romanesque, rows of arches go obliquely into the point of the roof and by this strong pointing toward the centre create an inward tendency. Six of the illustrations have the central arch accented by decoration; seven have heavier piers around the central and end arches; six have the end arches brought out into a nearer plane which effectually finishes the series. All these examples illustrate the necessary disposition of arches on a flat wall or façade where the series in the field of vision must end suddenly, that is, cannot gradually fade away around a corner. The variety and yet invariability of these devices shows the need felt for some finish at the end, some balance of the whole with the central accent, which need, apparently, is not felt for pillars and lintels.

When the arch-series is on a circular structure, such as apses, porches, and the like, even when it does not entirely surround it, as an arena or spire, the regular diminishing of the series on either side, owing to the curve, supplies the finish necessary, and the size and arrangement of the arches need not vary otherwise. Twelve of the examples illustrate such a use of the arch, and although in some cases, Morano Cathedral, Nomantala Church, the arches are continued into the transepts gradually tapering in size, or are modified in size growing narrower from the centre, as in the Bergamo Church, such a treatment is not necessary for finished effect. The difference in proportion resulting from a curved series, or even on arches carried around a square corner (as in porches on Goslar and Braunschweig Rathäuser), where the series is open enough to clearly see its continuity as it runs into the main building, will suffice to make a series finished without modifications of the arch-units.

There are many instances of long rows of very narrow arches on cathedral façades which are too narrow to give outward tendency, or else they have statues within them which really take the attention and form a series of vertical units in place of the arches. There is also the common device of interlacing arches, where a supporting pillar of another arch stands in the centre of every arch, thereby always driving the attention backward and restraining it. Perhaps the natural outward tendency of the arch-series and the necessity for its limitation can be seen by violations of the principle. Seven of the examples do not conform to any application of this rule and the results are not satisfactory so far as the mere series itself is concerned. Over the right and left doors of the Piacenza Cathedral are sections of nine arches which end abruptly and do not even meet each other. The Fredericksborg Schloss at Copenhagen has a row of fifteen arches enclosing a court. These run into wings on each side, to be sure, but all seen at once as they are and without central or end modification they are too sharply cut off and inclined to overstep their limits. The Loggia dei Lanzi at Florence, with its three wide arches and narrow pillars, the William Tell Chapel in Switzerland, with only two arches, illustrate forcibly the tendency of an arch to move outward, to appear too wide for the superstructure and too "active" unless bound down in some way. Four arches on the right and left of the façade of Marmonte Church, but not across the centre, have the same unfinished effect. The roman arch on one side of the St. Lo Cathedral façade with two gothic arches on the other defy every principle of repetition and symmetry as well.

From this survey of one hundred and sixty-five of arch-series we find through a variety of means a uniformity of purpose in their treatment; that all point to a common demand, however differently expressed, according to the function of the series. The series must be prevented from "running away." It must either run completely around a structure into itself, or be balanced as a whole so that the attention which naturally runs off the ends is driven towards the centre. This may be accomplished by enlarging, decreasing, decorating, or pointing toward centre of the arch by means of the obliquity of both halves of the series. It may also be brought by enlarging, decreasing, changing the plane of the end arches or altering the size of the limiting piers. The essential value of the arch may be altered by narrowing it, by filling it with something more important than itself, thereby making it only an attendant series upon its content, by interlacing it, or by any device that transforms or revises its outward tendency.