In 1609, Hudson was chosen by the Dutch East India Company to find an easterly passage to Asia.
After crossing the Atlantic Ocean, his ship, the Halve Maen (Half Moon), sailed around briefly in the Chesapeake and Delaware Bays, but Hudson concluded that these waterways did not lead to the Pacific. Hudson then moved into New York Harbor and proceeded up what is today the Hudson River. He made it as far as Albany, New York, where the river narrows, before he was forced to turn around, realizing that it was not the Southwest Passage. In fact, there is no Southwest Passage to the Pacific.
Henry Hudson, under strict orders to discover the north eastern passage to the orient, departed from Amsterdam. He completely disobeyed his instructions and after a brief pass along the coast of Norway followed a westward gale toward the North American continent.
On his quest for the northwest passage, Hudson was the first European to enter Delaware Bay. After sighting treacherous shoals and sand bars, he determined that this river was not the passage he was looking for and continued northward along the Atlantic coast.
"The Island at the Center of the World", pg 31, Russel Shorto, 2004, Vintage Books
He anchored off Manhattan Island on September 12, 1609, and continued up the river that bears his name, the Hudson River, until he arrived at the site where New York State's capital city, Albany, now stands.
http://en.wikipedia.org/wiki/Henry_Hudson
http://en.wikipedia.org/wiki/History_of_New_York_City#Lenape_and_New_Netherland:_prehistory_-_1664
He arrived in Albany sometime after September 12, 1609
On his return trip to Amsterdam, he stopped in Dartmouth, England for some reason and was detained by authorities there, who wanted access to his log. He managed to pass the log to the Dutch ambassador who sent it, along with his report, to Amsterdam.
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