Historians have said very late September or very early October. Here is a witness, more than half a century later:
John Sarrett W312: “eight days subsequent to which time [the day of the battle at Livingston’s Bridge] declarent was engaged in the battle of brown marsh, at a place called Baldwin’s plantation; during which engagement declarent lost his horse—this engagement was against the tories and some British also—in which we were defeated owing entirely, as declarant is of opinion, to the bad management of Gen Butler the commanding officer.”
If the battle at Livingston's Bridge was on September 23, 1781 and the battle at Brown Marsh was 8 days later, that would be
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October 1, 1781 for the date of the battle at Brown Marsh?
Does it matter? Come on, we want to know.