The western apse of the cathedral at Mayence is the most modern part of these three great cathedrals, and perhaps the only example in Germany where a triapsal arrangement has been attempted with polygonal instead of circular forms. In this instance, as shown in Woodcut No. 705, the three apses, each forming three sides of an octagon, are combined together so as to form a singularly spacious and elegant choir, both externally and internally as beautiful as anything of its kind in Germany. Its style is so nearly identical with that of the eastern apse of the cathedral at Trèves (Woodcut No. 698), that there can be no doubt but that, like it, it belongs to the beginning of the 13th century. At this time more variety and angularity were coming into use, suggested no doubt by the greater convenience which flat surfaces presented for inserting larger windows than could conveniently be used with the older curved outlines; for now that painted glass had come into general use, large openings had become indispensable for its display. Notwithstanding this advantage, and the great beauty of the other forms often adopted, none of them compensate for the external effect of the circular lines of the older buildings. [Illustration: 705. Western Apse of Cathedral at Mayence.] Proceeding northwards, we find in the churches of Westphalia a fine series of examples which are comparatively but little known. Among the more important of these we may mention Münster, with its fine and impressive nave, Soest, Paderborn, Lippstadt, Osnabrück, Hildesheim, Hameln, Hersfeld, Brunswick, Quedlinburg, Goslar, Gelnhausen, etc. They are very numerous, and many of them are sufficiently large for architectural effect; but in the earlier Romanesque work they are somewhat heavy, and in the age of the pointed Gothic style there is a tendency to attenuation which is the reverse of pleasing. In some of the early churches there is considerable refinement, as may be seen in the narthex porch of the cathedral of Soest (Woodcut No. 706); and in the Schloss Kirche at Quedlinburg there is a profusion of sculpture in the capitals, some of which show considerable Byzantine influence.