When the Pontifical Government returned to power in 1815, Pope Pius VII. ordered the enormous buttress to be built, for supporting one end of the wall then left broken, and preventing the ruin from extending further. We have already lost forty-seven out of the eighty arches, which have been destroyed for using the materials by previous Popes to build their family palaces, or monasteries and churches, so that there remain only thirty-three of the external arches of travertine. The other end of the wall, near the Meta Sudans, was left in a dangerous state until that was also supported by the great buttress of Leo XII. In 1828, Gregory XVI. followed the example of his immediate predecessors, and rebuilt in brick some arches of what had been the internal corridors, but had become external, owing to the demolition of the great outer arcades in earlier ages. In 1852, Pius IX. repaired the principal entrance from the Esquiline side, and some more of the arches of the inner arcade. Under the arena was all the machinery usual under the stage of a large theatre; and much space was required for it. When the boards had to be cleared off the central part, to leave open the four long channels of water, which are seen in the view of the Colosseum taken in 1812[159], and the space between them which was probably flooded to the depth of a few feet for effect, the boards removed from the centre must have been piled up at the sides, and on the large corbels before mentioned[160]. Apollodorus, the architect, in his celebrated reply to the Emperor Hadrian, told him that _he ought to have_ prepared a place for the machinery of the great amphitheatre under the platform, and in such a manner that the great building should have been visible from the Forum Romanum. The site intended by him for the temple evidently was the large level platform on the Summa Sacra Via, on which S. Francesca Romana now stands; and the place for the machinery intended by him was obviously that excavated in the spring of 1874, under the south-east end of the platform immediately opposite to the Colosseum, a very convenient place for the purpose. There still remains a rude rubble vault, of the time of the Republic, with a small aqueduct introduced in the time of the early Empire to carry water to the fountains at each corner of the Porticus Liviæ, which must have been on this site, but which did not extend to the end. There is an excellent place for a temple at the end of the _porticus_ or colonnade; and the platform could easily have been extended several yards nearer to the Colosseum: it is evident that this is what Apollodorus said that Hadrian _ought to have done_, but that he had not done so.