What makes the island fly?

In Part III, chapter 3, Gulliver is traveling in Laputa. Swift gives very specific descriptions about this unusual floating island:

The island is exactly circular, its diameter 7837 yards, or about four miles and a half, and consequently contains ten thousand acres. It is three hundred yards thick.

Gulliver tells the prince that he would like to "know, to what cause, in art or in nature, it owed its several motions," and the prince provides him with a tutor to help him understand how the island functions. From his tutor, he learns that the island has a "loadstone of a prodigious size, in shape resembling a weaver's shuttle," and this serves as a magnet. By this magnet, with its attractive and repulsive ends, the inhabitants navigate the floating island where the ruler wishes.
The magnet does have its limits, though. For instance, it cannot go beyond the height of four miles. The Laputian scientists explain this by saying that the "magnetic virtue does not extend beyond the distance of four miles." This concept, of a floating island, doesn't seem tremendously out of the ordinary to modern readers who are used to airplanes. However, Gulliver's Travels was published in 1726, many years before air travel was imagined. In fact, even untethered hot air balloons were not used until the late 18th century. (Additionally, hot air balloons are not flown much more than two miles above the ground.) The idea of a floating island would have been other-worldly (and probably fairly exciting) to early 18th century readers.