æsthetic unity and care put upon it to make it beautiful for its own sake, it must not be thought of as the _end_ of any series. It must be cut off from the rest of the world by supports or framed in some way, and while it still may have a place in a series, provided it is sufficiently conventionalized and not too important in itself, it must not be thought of as either ending or beginning, as depending on a series to give it importance, or lending support to anything else. It simply exists, cut off from the world, even though in the balustrade not an integral part of it, and one ought to be able to remove it without affecting the stability of the structure. The question whether series of symmetrical units have less heavy ends to finish them than series of rhythmic units cannot be settled by these methods of analysis. While it seems certain that the rhythmic series drives the attention on by its greater motor activity, and hence would need more of an end to stop it, so many other factors enter in of more importance, such exact measurements would be necessary (quite impossible with the photographs of the scale here used), the refinement would be so great, since the stone of which most of the examples are made, by its own weight supplies a check to rhythmic activity, all these considerations make it impossible to illustrate this conclusion and it must remain an experimental result alone. There remains one question: Is regular repetition of three units ever found? They may be in combination of some kind so that they fall into a rhythm of twos, but are they ever found repeated as three separate and distinct units? The answer to this is without exception. Of the five thousand photographs analyzed, not one instance of this kind of series was found. In many cloisters the pillars are of different design, and often one design is repeated through an otherwise varying series, but their repetition is either without scheme of any kind, or in some combination that falls into a rhythm of twos. No three-rhythm has been used in art, any more than it has been found possible in experiments. ARCHES