It took place on the island of Saint Croix in August 1772. Hurricane season.
Here is some context, courtesy of the Library of America:
Alexander Hamilton first came to public attention at the age of seventeen. His father had abandoned the family when Alexander was ten, and his mother died four years later. He was effectively an orphan, working as a clerk for a mercantile firm on the island of Saint Croix at the end of August 1772, when a major hurricane, one of the strongest of the century, roared through the Caribbean. Nearly every ship at harbor was swept aground, some as far as 100 yards inland, and giant boulders and rockslides came crashing down from the surrounding hills. An account written later in the year details the damage to each of the islands. In St. Croix, “every house almost at Christianstadt [the island’s capital city], and all the plantations and negro-houses levelled. Only three houses left standing at Frederickstadt, and numbers of people killed.” After striking the islands, the storm then continued its path of destruction along the Florida panhandle, the Alabama coast, and New Orleans. Some meteorologists have categorized this catastrophe, with its extraordinary storm surge, as a tsunamic hurricane.
A week later Hugh Knox, a Presbyterian minister who had immigrated to Saint Croix earlier that year, delivered a sermon to the island’s frazzled population. After the service Alexander, profoundly impressed by Knox’s oration, went home and wrote a letter to the father he had not seen for nearly seven years. “Hamilton did not know it, but he had just written his way out of poverty,” remarks biographer Ron Chernow. The young man apparently showed the letter to Knox, who doubled as a journalist and occasional editor for The Royal Danish American Gazette, a newspaper established two years earlier and distributed widely throughout the West Indies.
Read the entire introduction here.
The letter, dated September 6, 1772, began:
Honoured Sir, St. Croix, Sept. 6, 1772
I take up my pen just to give you an imperfect account of one of the most dreadful Hurricanes that memory or any records whatever can trace, which happened here on the 31st ultimo at night.
It began about dusk, at North, and raged very violently till ten o’clock. Then ensued a sudden and unexpected interval, which lasted about an hour. Meanwhile the wind was shifting round to the South West point, from whence it returned with redoubled fury and continued so ’till near three o’clock in the morning. Good God! what horror and destruction. Its impossible for me to describe or you to form any idea of it. It seemed as if a total dissolution of nature was taking place. The roaring of the sea and wind, fiery meteors flying about it in the air, the prodigious glare of almost perpetual lightning, the crash of the falling houses, and the ear-piercing shrieks of the distressed, were sufficient to strike astonishment into Angels. A great part of the buildings throughout the Island are levelled to the ground, almost all the rest very much shattered; several persons killed and numbers utterly ruined; whole families running about the streets, unknowing where to find a place of shelter; the sick exposed to the keeness of water and air without a bed to lie upon, or a dry covering to their bodies; and our harbours entirely bare. In a word, misery, in all its most hideous shapes, spread over the whole face of the country. A strong smell of gunpowder added somewhat to the terrors of the night; and it was observed that the rain was surprizingly salt. Indeed the water is so brackish and full of sulphur that there is hardly any drinking it.
Read the entire letter here.