Rochambeau began his march from Newport on the 10th of June, leaving at that place a sufficient garrison, its harbor being still occupied by French ships of war. Washington assembled his troops from their different encampments on the west side of the Hudson, brought them across King's Ferry, and ou the 2(>th established his headquarters at the Van Cortlandt house north of Peekskill. lie at once proceeded to demonstrate to the British that the joint movement was not a mere feint or a venture whose final object was to be approached gradually, but a swift and deadly undertaking against New York. The promptitude with which Washington, after arriving at Peekskill, planned and executed the demonstration on New York, and the fine judgment with which he arranged his combinations, must have been convincing proof to Sir Henry Clinton that he would soon be called upon to defend the city with all the resources at his command. Washington had two immediate objects in view -- first, to surprise and, if possible, capture the British position at Kingsbridge; second, to cut off de Lancey's large body of Refugees at Morrisania and any other troops of the enemy north of the Harlem River. The two schemes were to be carried out simultaneously and with great secrecy and rapidity. The Kingsbridge enterprise was to be under the charge of General Lincoln, of the American army, who was to drop down the river under cover of night, reconnoiter the works at the northern end of Manhattan Island, and, if he found them not too strongly defended, attack Kingsbridge. At the same time the Duke de Lauzun, of the French army, was to come down to Morrisania from Connecticut by a forced march and fall upon de Laneey. In the event that Lincoln should find it imprudent to attack Kingsbridge, he was to take a station near that place so as to prevent de Laneey from escaping to Manhattan Island.