Immediately after their successful passage up the river, the General wrote to the Governors of Connecticut and Rhode Island, for the use of some of the galleys which those States had built; and, on the twenty-fourth of July, he wrote to the Convention of New York, telling it what he had done ; that he was in expectation, "every ''hour," that three or four of those galleys would reach the City of New York ; that he had one, ali-eady ; that if any measures were being taken for attacking the ships, in which these galleys could be usefully employed, to let him know ; and that, " if not other- " wise materially engaged," he should be glad to cooperate with them, and to furnish any a-ssistance which the galleys could give.'" The reply of "the "Secret Committee" of the Convention, to whom this portion of the General's letter was referred, has not been found ; but the tenor of it may be seen in the fact that two of the galleys went up the river, on the twenty-eighth of July, and three or four more on the first of August; " and that they probably " ran into "shoal water and creeks, whence they could warp out, " at certain times of tide, and annoy the shipping." On the afternoon of the third of August, these galleys -- bearing the names, respectively, of Wa)<hin(/toii, Laily Wtishingtou, Spifjifc, W/iifiii;/, Independence, Crane, and an unnamed whaleboat -- boldly attacked the ships, at their anchorage ; and as this early naval conflict occurred in the waters of Westchestercounty, we make room for the contemporary account of it: