4. One room on the upper floor of the palace shows a fuller comprehension of the thrust and buttressing of the vault (room No. 12, _Hatra_, ii, Plate 10 and Fig. 226). The space to be covered is diminished by placing two arched niches on either side, a system which points the way to the breaking up of the wall into buttressing piers. This principle was carried out yet further by Sasanian builders. In the palace of Sarvistân the lower portion of the piers was detached from the body of the wall and further lightened by being divided into two small columns,[112] while angle piers terminating in a single detached column bore the dome of a chamber situated at the back of the palace (Plate 74, Fig. 1). The advance in structural knowledge thus gained was carried little further in these regions; indeed it is curious to observe that Ukhaiḍir exhibits a movement in the opposite direction. Although in rooms 33 and 40 the vaults are set upon columns which stand absolutely free, the vault of the great hall rests upon arched niches whereof the piers are connected with the wall, and the principle of the detached column is recalled only by the engaged columns which form part of the pier. The arcade on free standing columns with a vaulted corridor behind it is of frequent occurrence, but the fact that in all the palace only one, and that one the shortest, of these arcades remains standing (No. 20) shows that the skill of the builders was at fault. Again, in the church of Mâr Ṭahmâsgerd at Kerkûk the engaged columns are present, as in the great hall of Ukhaiḍir, but in the same manner they are structurally one with the piers behind them[113] (Plate 75, Fig. 1); and in the churches of northern Mesopotamia, where deep niches under the vault are a constant feature, the engaged pier of Hatra returns in all its primitive simplicity.[114] Whether the data afforded by extant monuments in Mesopotamia and Persia are conclusive would be hard to determine. The setting of arch, vault, and dome on free standing supports would seem to have been a conception deeply rooted in Hellenistic art, but for actual examples we can adduce only the evidence of relief architecture or the disposition of rock-cut tombs and temples. The blind order under the vault of the men’s caldarium near the forum at Pompeii,[115] the rock-cut dome on engaged columns of the Hellenistic tomb of Akeldama at Jerusalem[116] exhibit a motive to which the architecture of a later age was to give fully developed plastic execution. Yet more explicit are the indications afforded by the rock-cut monuments of Egypt and of India. At Memphis one of the graves of the Persian period shows a vaulted nave resting on piers,[117] and the rock-cut temples of Hellenistic India, with their long vaulted naves resting on columns,[118] point to similar achievements in the Seleucid architecture of Mesopotamia from which they are derived. The existence of an underlying desire to solve statical problems which were of the