Further southwards at the foot of the slope we come to another fragment of the most ancient wall of the Palatine settlement. This building appears to stand at right angles to the line of the hillside, and it was therefore supposed at first to have belonged to a wall traversing the intermontium or depression which crosses the Palatine Hill from this point to the Arch of Titus, and to have confirmed the opinion of those archæologists who confine the extent of Roma quadrata to the north-western end of the hill. But subsequent exploration has shown that this wall does not pass along the intermontium, but turns off at a right angle. Another fragment of the most ancient wall was found in 1860, according to Lanciani, under the Villa Mills, showing that the wall of Roman quadrata passed round the whole hill, and not only round the north-western end. [Sidenote: Domus Gelotiana.] Close to the fragment of ancient wall we come to a series of chambers excavated first in 1857, and afterwards cleared and rendered more accessible in 1869. These belonged to a building in connection with this part of the imperial palace, and were occupied by soldiers of the emperor’s guard, as may be seen by examination of the inscriptions left on the walls. The traces of a square court, surrounded with a portico, one granite pillar of which remains, and on the side of this court towards the hill, of a number of chambers arranged on each side of a semicircular recess, are the main features of this ruin. The brickwork supports which appear here were erected by Canina, and a large quantity of remains have fallen from the higher levels of the hill. The inscriptions which are most remarkable are the following. On the right-hand wall near the entrance the name HILARUS, followed by the letters MI. V. D. N., which have been interpreted to mean “miles veteranus domini nostri,” a veteran soldier of our Lord. Numerous other inscriptions with the letters V. D. N. will be found in the chamber to the left of the central recess. One of these in the triangular room records the name of two soldiers who belonged to the foreign troop of Peregrini: BASSUS ET SATURUS PEREG.[11] Other inscriptions allude to a pædagogium, or training school, as for example, CORINTHUS EXIT DE PEDAGOGIO. Most of these are in the triangular rooms behind the central semicircular recess, or in the furthest room on the left of it. In this last is to be seen the figure of an ass turning a mill, with the inscription, LABORA ASELLE QUOMODO EGO LABORA VI ET PRODERIT TIBI. But the most famous of these graffiti is that now shown in the Kircherian Museum representing the crucified ass, with the title “Alexamenus worshipping his god,” which was taken from the room on the right of the central semicircular recess, and has been the subject of much comment. Another record of the same Alexamenus was found here in 1870, in which he is called Alexamenus fidelis. [Sidenote: Stadium.]