"A science fiction story is a story built around human beings, with a human problem and a human solution, which would not have happened at all without its scientific content."
- Theodore Sturgeon

The island's altitude and progress is determined by magnetic levitation:

At the Centre of the Island there is a Chasm about fifty Yards in Diameter... The greatest Curiosity, upon which the fate of the Island depends, is a Loadstone of a prodigious size, in shape resembling a Weaver's Shuttle. It is in length six Yards, and in the thickest part at least three Yards over. This Magnet is sustained by a very strong Axle of Adamant passing through its middle, upon which it plays, and is poised os exactly that the weakest Hand can turn it...

By means of this Loadstone, the Island is made to rise and fall, and move from one place to another. For, with respect to that part of the Earth over which the Monarch presides, the Stone is endured at one of its sides with attractive Power, and at the other with a repulsive. Upon placing the Magnet erect with its attracting end toward the Earth, the Island descends; but when the repelling Extremity points downwards, the Island mounts directly upwards. When the Position of the Stone is obliqe, the Motion of the Island is too.

By this oblique Motion the Island is conveyed to different Parts of the Monarch's Dominions.

See another use of this idea in Islands in the Air (1929) by Lowell Howard Morrow, in particular the deflector that makes it possible.

('Islands in the Air' by Lowell Howard Morrow)