The ribs of a Byzantine dome are not constructive in the same way as are the ribs of a Gothic vault. They were built along with the rest of the dome and of the same material, and are in no way separate from the infilling, though they no doubt strengthened the shell of the dome by their form[28]. On the outside a circular shaft with a very simple cap is often placed at the angles of the piers, and from these shafts the brick cornice springs in a series of arches over the windows. Sometimes the angle is formed by a point between two half-shafts, as in the domes of the narthex in S. Theodore (p. 246). _External Treatment._--In the older churches the exterior seems to have been left in simple masses of brickwork, impressive only by their size and proportion. Probably even this effect was not considered of great importance. In later times a very beautiful system of decoration with slender shallow niches was introduced and was applied in particular to the east end and to the apses. The finest examples of this system on a large scale are seen at the Pantokrator (p. 235) and S. Theodosia (p. 173). Carefully considered or elaborate external compositions are rare, and the only examples in Constantinople are the side chapel of the Pammakaristos (p. 154) and the narthex of S. Theodore (p. 246). _External Marble and Mosaic._--Marble and mosaic, we have reason to know, were occasionally used on the exterior of churches,[29] though no fragments remain. On the south side of the Pantepoptes (p. 216) the string-course does not correspond to the line of the walls, but projects in a manner which shows that marble must have been employed to line the large windows. A similar projection of the string-course or cornice is not uncommon elsewhere, though not so evident as in the Pantepoptes, and may have been made to receive a marble or mosaic lining. _Doors and Windows._--It is a primary rule in Byzantine architecture that all constructive openings are arched. Whatever may be the eventual form of a door or window the opening is first built in brick with a semicircular head, and into this opening the marble jambs and lining are fitted leaving a semicircular lunette above. Doors are square-headed, with heavily moulded architraves and cornice, and the lintel is mitred into the jambs instead of having the more constructive horizontal joint used in the West.