And to the end that justice may be done, in cases civil as well as criminal, and against persons offending upon the said river, or upon any island or dry land within the same, and belonging to this commonwealth: The bed of the same river, and the islands and dry land within the same, so as aforesaid assigned to and belonging to this state, lying and being northerly of a north-easterly line from the extremity of the boundary line between the counties of Bucks and Northampton, at the bank of the river Delaware, to be extended across the said river unto the shore of New Jersey, shall be deemed to be, and shall be henceforth, parts of the county of Northampton, and of the several adjoining townships and precincts of the same county, lying along the said river.