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. 165 _Examples of Arch-Series._