At least one of these structures still existed in 1898 when Förster visited the site. He makes the following reference to it in a footnote:
"Ein solches Wasserreservoir erkenne ich auch in der am Fusse der jetzigen Burgruine gelegnen Mulde von amphitheatralischer Form (Durchmesser: 70 Schritt), deren Umfassungsmauer aus Bruchsteinen mit einer Zwischenlage von Ziegeln besteht".
He goes on to quote Procopius in De Aedificiis:
"αλλα χαι βαλανεια χαι υδάτων ταμιεια εν τοις δρεσι πεποιηται τούτου του τειζουζ εντός"
And then notes that in Guidi's translation of the Vatican Arabic Manuscript (which he insists on terming Zeineddini) : "... nel monte di essa citta evvi una casa (serbatoio) di acqua, chiamato in lingua greca b. lût. sa (Balaneion?) e 'acqua ne scatusice da una rupe dura; chi si bagna in essaai 21 di Adar (Marzo), gli e giovenole, lo guarisce da elefantiasi e lebbra col permesso di Dio altissimo".
One can't think much of ancient hygeine (who does?) to find the victims of elephantiasis and leprosy bathing in the town reservoir as a "cure"!
Forster goes on to cite Malalas on the theme of this structure: "Theodosios hatte die von Caesar für das öffentliche Bad hier angelegte Wasserleitung abgebrochen".
He cites Pococke and Poujoulat's works as positing: "...berichten von einer Sage, dass die römischen Kaiser sich in diesem Bassin mit Kahnfahren vergnügt hätten."
Then Chesney claiming the site was: "...traditionally connected with the Pagan immolations to Jupiter".
Ritter in Erdkunde is mentioned as saying: "..hat daraus --ein Felsenamphitheater con 90 Fuss im Durchmesser, das die Sage einen Opfernplatz des Jupiter nannte-- gemacht und es in der Nahe des Charonion gesetzt".
The demise of the amphitheatre (Monomachio) is intriguing because Malalas speaks of it being demolished to build the Theodosian Walls: "Murum vero novum perduxerunt etiam ad Phurminum, quod vocant, fluentum, ex montis cavernis emanans; comportatis eo lapidibus ex Monomachio veteri, quod superius ad Acropolim stetit. Dirutus est etiam, quem Julius Caesar extruxerat, Aquaeductus, aquas ex via Laodicena ad Acropolim deferens, ad Ваlneum aquis supplendum, quod ad montem extruxerat, in usum Acropolitarum , qui sedes ibi olim posuerant, reliquique fuerunt ex eis, quos Nicator Seleucus, in planiciem deductos, adhortatus est, uti sedes, ubi et ipse ponentes, urbem a se conditam, Ântiochîam magnam incolerent". If this was demolished in Theodosius' time then what were the later travellers looking at?
All this information is typical of the garbled historical accounts. Wilber/Downey has the amphitheater way over near the Southern wall, the Charonion is on the north side on the city. The sacrificial place for Jupiter we have heard spoken of before as being near the Temple of Zeus Keraunios. This was in Iopolis (one of the "four cities" within Antioch) and presumably also near the Southern wall.
Was this a reservoir, an amphitheater (as was so common in Roman cities for gladiatorial combats) or a naumachia (a place for mock naval battles)? Antioch surely had an amphitheatre, but why should it have been perched on the side of the mountain? That is not traditional in Roman city building. Usually the amphitheatre was on the level terrain, frequently outside the city walls. We can see why it could be either a reservoir (serving double duty as a naumachia) due to the constant flow of water along the aqueducts arriving in the city from Daphne.