How and when did Gulliver's second voyage begin?
In part II, chapter 1, In Gulliver's own words, he took the second trip as a result of being restless and wanting an active lifestyle. Two months after having arrived in England, he was already on cue for another adventure.
I again left my native country, and took shipping in the Downs, on the 20th day of June, 1702, in the Adventure, Captain John Nicholas, a Cornish man, commander, bound for Surat.
After a huge storm, a series of interruptions, and the usual issues that occur at sea, Gulliver tells us that a mass of land was finally spotted. This was the beginning of his adventure at Brobdingnag.
On the 16th day of June, 1703, a boy on the top-mast discovered land. On the 17th, we came in full view of a great island, or continent (for we knew not whether;) on the south side whereof was a small neck of land jutting out into the sea, and a creek too shallow to hold a ship of above one hundred tons.
Contrary to Lilliputians, the Brobdingnagians are huge people who demean Gulliver's rather small size sort of like the way he felt for the Lilliputians, to whom he was a giant. During this travel, Gulliver gets humilliated in many ways. He is used as a slave, he is treated badly, and he actually gets to miss the Lilliputians.
I bemoaned my desolate widow and fatherless children. I lamented my own folly and wilfulness, in attempting a second voyage, against the advice of all my friends and relations...... I could not forbear thinking of Lilliput, whose inhabitants looked upon me as the greatest prodigy that ever appeared in the world
In a rare moment of self-deprecation, Gulliver actually thinks of those friends and family whom he never listens to, and who seem not to get the better of him when it comes to making choices between staying with them or enter the unknown. After having being treated almost like a godlike entity in his former trip, Gulliver definitely gets slightly humbled by this experience. However, it is clear that he will do more voyages in the future.
Gulliver's second voyage begins two months after his first one (island of the Lilliputians). During the second voyage, he visits the Brobdingnagians people, who are giants.
There, Gulliver is treated like an outcast and freak; he is forced to fight animals savagely. He finally returns to England after an eagle drops him off in the middle of the ocean and a ship rescues him.