The absence of the dome at Hatra is significant. The small square chambers of the palace were well suited to dome construction, yet nothing but the barrel vault is present. Moreover, it is the barrel vault in its simplest expression; not even an intersection is attempted. In the vaulted passage surrounding the central chamber of the western annex, the ‘temple’, one end of the vault terminates on each of the four sides against a transverse arch, whereby the insuperable difficulty of intersection was avoided[124] (Plate 75, Fig. 2). Hellenistic builders had attacked the problem as early as the second century B.C. in Asia Minor,[125] and yet more boldly in Rome.[126] I know no single example of the intersection of barrel vaults in Sasanian buildings; even at Ukhaiḍir the system is sparingly used, and never without careful abutment. Where two barrel vaults meet at right angles, they are either joined together diagonally, without intersection, as in the chemin de ronde, or they terminate against transverse arches, and not infrequently in the rectangular space thus formed, a semi-dome takes the place of the intersecting vault, as in the mosque and in the upper gallery No. 134. The rock-cut temples of India exhibit a similar termination of the barrel vault in a semi-dome.[127] The dome, though it is at Ukhaiḍir of frequent occurrence, the chambers of the chemin de ronde in all the round towers being domed as well as the two chambers north and south of the great hall, Nos. 4 and 27, is never placed over a span wider than 3·10 metres. The square rooms, Nos. 30 and 141, behind the two lîwâns 29 and 140, where, on the analogy of the Sasanian palaces (see below, pp. 74, 76 and 78) a dome might be expected, are covered in one case by a barrel vault, and in the other case by a groined vault. There was no question here of a dome on free standing columns; where the opportunity occurred, in rooms 33 and 40, it was set aside in favour of parallel barrel vaults. The domed chambers in the towers have a circular ground-plan, and when the problem presented by the rectangular substructure arose, it was met in a fashion which is applicable only to very small edifices. The dome in No. 4, and all the calottes over rectangular niches, are set over the angles upon horizontal brackets of masonry. On the octagon, or half-octagon, thus formed, a circle or segment of a circle of small diameter could be placed without any difficulty. It was an expedient which had been adopted by early dome builders both in Syria and Asia Minor,[128] but it was inadequate when the space to be covered assumed larger dimensions and, before the date of Ukhaiḍir, Byzantine and Sasanian architects had elaborated solutions of the problem. In the West the great dome of Santa Sofia had already been placed securely upon stone pendentives; in Persia the use of the arched angle niche, or squinch, had enabled Sasanian builders to throw their domes over a span of 16 metres.