We fetched a compass - We coasted about; or we sailed along the eastern side of Sicily.
And came to Rhegium - This was a city of Italy, in the kingdom of Naples, on the coast near the southwest extremity of Italy. It was nearly opposite to Messina, in Sicily. It is now called "Reggio."
The south wind - A wind favorable for their voyage.
To Puteoli - The wells. This place was celebrated for its warm baths, and from these and its springs it is supposed to have derived its name of The Wells. It is now called "Pozzuoli," and is in the campania of Naples, on the north side of the bay, and about 8 miles northwest from Naples. The town contains at present (circa 1880's) about 10,000 inhabitants.

We fetched a compass - Ὁθεν περιελθοντες, Whence we coasted about. This will appear evident, when the coast of Sicily is viewed on any correct map, of a tolerably large scale.
Rhegium - A city and promontory in Calabria, in Italy, opposite to Sicily. It is now called Reggio. It had its name, Ῥηγιον, Rhegium, from the Greek Ῥηγνυμι, to break off; because it appears to have been broken off from Sicily.
The south wind blew - This was the fairest wind they could have from Syracuse, to reach the straits of Rhegium.
The next day to Puteoli - This place, now commonly called Pozzuoli, is an ancient town of Naples in the Terra di Lavoro; and is supposed to have been founded by the Samians, about 470 years before Christ. Within this city are several warm baths, very highly celebrated; and from these, and its springs in general, it seems to have had its ancient name Puteoli, from Putei, wells or pits; though some derive it from putor, a stench, or bad smell, because of the sulphureous exhalations from its warm waters. Varro gives both these etymologies, lib. iv. de Ling. Lat. cap. 5. It is famous for its temple of Jupiter Serapis, which is built, not according to the Grecian or Roman manner, but according to the Asiatic. Near this place are the remains of Cicero's villa, which are of great extent. The town contains, at present, about 10,000 inhabitants. Long. 14. 40'. E., lat. 41. 50'. N.

And from thence we fetched a compass,.... About the isle of Sicily, from Syracuse to Pachinus, the promontory of the island:
and came to Rhegium; a city in Calabria, called by Ptolomy (k) Regium Julium; it was built, as Solinus (l) says, by the Chalcidensians, and was formerly a city of the Brutians (m); it is now called Reggio: it is said (n) to have its name from its being broken off from the main continent, for it lies in the straits of Sicily; and formerly Sicily was joined to Italy, but was separated from it by the violence of the sea at this place:
and after one day the south wind blew; they stayed one day at Rhegium, and when they departed from thence, they had a south wind, which was favourable to them: whether the apostle preached here, or no, is not certain, since his stay was so short; some Popish writers tell some idle stories about the apostle's preaching; how that the fishes came to the shore to hear him; that the grasshoppers were commanded by him to be silent, and have never been seen in that place since; that a stone pillar was set on fire by the flame of a candle, by which miracle the inhabitants present were converted and baptized; and one Stephen, that was in company, was made by him their first bishop: but in ecclesiastical history we meet with no account of any church in this place, until the fifth century; when the bishop of it, with others, subscribed a letter of Leo the First, sent into the east; and about the year 440, there was a synod of thirteen bishops convened in this place, on account of a certain ordination; and in the "seventh" century, a bishop of the church at Rhegium was present in the sixth council at Constantinople; in the "eighth", Constantine, bishop of Rhegium, was in the Nicene synod (o):
and we came the next day to Puteoli; the Syriac version adds, "a city of Italy"; it was formerly called Dicearchia (p), from the strict justice used in the government of it: it had its name of Puteoli, either "a putore", from the rankness and ill smell of the waters of it, through the "sulphur" and "alum" in them; or "a puteis", from the wells about it, the waters of which, by Pausanias, are said (q) to be so hot, as in time to melt the leaden pipes through which they flow, who calls it a town of the Tyrrhenians; by Pliny (r) it is placed in Campania, and so Jerom (s) says, Puteoli a city, a colony of Campania, the same that is called Dicearchia. Josephus (t) also speaks of it as in the same country; for he says, that Herod and Herodias both came to Dicearchia, (or Puteoli), and found Caius (the emperor) at Baiai, which is a little town in Campania, about five furlongs from Dicearchia; and he also in another (u) place says, the Italians call Dicearchia, "Potioli"; which is the same word the apostle here uses, and which is the Latin "Puteoli" corrupted; it is said to be first built by the Samians: frequent mention is made by writers (w), of "pulvis Puteolanus", the dust of Puteoli; which being touched by the sea water, hardens into a stone; and was therefore used to bank the sea, break the waves, and repel the force of them: that it was a place by the sea side, may be learned from the sea being called after its name, "mare Puteolanum" (x), the sea of Puteoli; so Apollonius Tyaneus is said (y) to sail from this place to Rome, whither he came in three days; to this port the ships of Alexandria particularly used to come, and hither persons were wont to go to take shipping for Alexandria (z); it is now called by the Italians Pozzuolo, and lies about eight miles from Naples; and according to the following story of the Jews', must be an hundred and twenty miles from Rome; who tell us (a), that
"Rabban Gamaliel, and R. Eleazar ben Azariah, and R. Joshua, and R. Akiba, went to Rome, and they heard the noise of the multitude at Rome, from Puteoli, an hundred and twenty miles:''
the story is a fable designed to signify the vast number of people at Rome, and the noise, hurry, and tumult there; but perhaps the distance between the two places may not be far from truth: and as fabulous is the account which R. Benjamin (b) gives of this place Puteoli, when he says it was called Surentum, a great city which Tzintzan Hadarezer built, when he fled for fear of David.
(k) Geograph. l. 3. c. 1. (l) Polyhistor. c. 8. (m) Mela, l. 2. c. 11. (n) Philo quod mundus, &c. p. 963. & de mundo, p. 1171. Vid. Justin. l. 4. c. 1. & Sallust. fragment. p. 147. (o) Ib. cent. 5. c. 2. p. 7. c. 9. p. 508. cent. 7. c. 2. p. 5. cent. 8. c. 2. p. 5. (p) Plin. l. 3. c. 5. (q) Pausan. Messenica vel. 1. 4. p. 285. & Arcadica vel. l. 8. p. 465. (r) Nat. Hist. l. 31. c. 2. (s) De locis Hebraicis, fol. 76. G. (t) Antiqu. l. 18. c. 8. sect. 2. (u) In Vita sua, sect. 3. p. 905. (w) Plin. l. 35. c. 13. Alex. ab Alex. l. 5. c. 9. Isidor. de origin l. 16. c. 1. p. 135. (x) A. Gell. noct. Attic. l. 7. c. 9. (y) Philostrat. Vit. Apollon. l. 7. c. 8. (z) Philo in Flaccum, p. 968. & de leg. ad Caium, p. 1018. Senec. cp. 77. (a) Echa Rabbati, fol. 59. 4. & T. Bab. Maccot, fol. 24. 1. (b) Itinerar. p. 14.

from thence we fetched a compass--that is, proceeded circuitously, or tacked, working to windward probably, and availing themselves of the sinuosities of the coast, the wind not being favorable [SMITH]. What follows confirms this.
and came to Rhegium--now Reggio, a seaport on the southwest point of the Italian coast, opposite the northeast point of Sicily, and at the entrance of the narrow straits of Messina.
after one day the south wind blew--a south wind having sprung up; being now favored with a fair wind, for want of which they had been obliged first to stay three days at Syracuse, and then to tack and put in for a day at Rhegium.
the next day to Puteoli--now Pozzuoli, situated on the northern part of the magnificent bay of Naples about one hundred eighty miles north of Rhegium, a distance which they might make, running before their "south wind," in about twenty-six hours. The Alexandrian corn ships enjoyed a privilege peculiar to themselves, of not being obliged to strike their topsail on landing. By this they were easily recognized as they hove in sight by the crowds that we find gathered on the shore on such occasions [HOWSON].