Under the guidance of this strange interpretation of Sozomon’s statement, the indefatigable explorer of the ancient sites of Constantinople set himself to discover the precise locality which the Hebdomon had occupied. As the suburb was in existence before the erection of the Theodosian Walls, the specified distance of one mile had to be measured from the original limits of the city, viz. from the Wall of Constantine. This, Gyllius thought, would put the suburb somewhere in the neighbourhood of the Walls of Theodosius. Searching next for more definite indications, he found the ruins of a splendid church dedicated to St. John the Baptist on the Sixth Hill, at Bogdan Serai near Kesmè Kaya. But a church of St. John the Baptist, as already intimated, adorned the Hebdomon, and so Gyllius leaped to the conclusion that the Hebdomon was the district on the Sixth Hill: “Suburbium Hebdomon appellatum in sexto colle fuisse, qui nunc est intra urbem, ostendit ædes Divi Joannis Baptistæ, quam etiam nunc Græci vulgo vocant Prodromi.” Having adopted this conclusion, it only remained for Gyllius to explain how a suburb only one mile from the city could have been styled the Hebdomon. His explanation is that the extramural territory along the Wall of Constantine had been occupied, before its enclosure within the Theodosian lines, by a series of suburbs distinguished from one another by numerals, and that the Hebdomon was so named because it was the seventh suburb in the series. This explanation he supports by pointing to the undoubted fact that one portion of that territory is frequently named the Deuteron[1189] by Byzantine writers. And he might have added that other portions of the territory were, respectively, styled the Triton[1190] and the Pempton.[1191] Du Cange[1192] was unable to accept Gyllius’s interpretation of the phrase, Ἑβδόμῳ Μιλίῳ. He insists upon its correct and only signification; and admits that the suburb derived its name from its situation near the seventh milestone from the capital. Nevertheless he is, impossible though it may seem, in substantial agreement with Gyllius. The fundamental thesis of Du Cange on the subject is that the term “Hebdomon” had two meanings. Strictly speaking, he grants, it meant the seventh mile; but it was also employed, he maintains, as the designation of the whole district extending between the Wall of Constantine and the seventh milestone. Hence, after the erection of the Theodosian Walls, a considerable portion of the suburb was included within the new city limits, so that the Hebdomon could very well be where Gyllius supposed it stood.