It was the Island of Tiboulen.

Dantes rose, advanced a few steps, and, with a fervent prayer of gratitude, stretched himself on the granite, which seemed to him softer than down.

Then, in spite of the wind and rain, he fell into the deep, sweet sleep of utter exhaustion.
At the expiration of an hour Edmond was awakened by the roar of thunder.
The tempest was let loose and beating the atmosphere with its mighty wings; from time to time a flash of lightning stretched across the heavens like a fiery serpent, lighting up the clouds that rolled on in vast chaotic waves.
Dantes had not been deceived--he had reached the first of the two islands, which was, in fact, Tiboulen.

He knew that it was barren and without shelter; but when the sea became more calm, he resolved to plunge into its waves again, and swim to Lemaire, equally arid, but larger, and consequently better adapted for concealment.
An overhanging rock offered him a temporary shelter, and scarcely had he availed himself of it when the tempest burst forth in all its fury.
Edmond felt the trembling of the rock beneath which he lay; the waves, dashing themselves against it, wetted him with their spray.

He was safely sheltered, and yet he felt dizzy in the midst of the warring of the elements and the dazzling brightness of the lightning.