Beginning September 14 de Grasse transported Washington and de Rochambeau’s men down the Chesapeake to Virginia, where they joined Lafayette and completed the encirclement of Yorktown on September 28. De Grasse landed another 3,000 French troops carried by his fleet. During the first two weeks of October, the 14,000 Franco-American troops gradually overcame the fortified British positions with the aid of de Grasse’s warships. A large British fleet carrying 7,000 men set out to rescue Cornwallis, but it was too late Although the war persisted on the high seas and in other theaters, the Patriot victory at Yorktown effectively ended fighting in the American colonies. Peace negotiations began in 1782, and on September 3, 1783, the Treaty of Paris was signed, formally recognizing the United States as a free and independent nation after eight years of war.