The jurisdiction of this commonwealth, and of the respective counties to which the bed of the same river, and the islands and dry land within the same, is by this act annexed as aforesaid, as far as the same shall be consistent with the agreement herein before recited, made between the states of Pennsylvania and New Jersey, shall be full and complete; and all writs and warrants, and process, duly issued within the said counties respectively, shall have force and operation, and may be executed with the river, islands and dry land, as parts of the same counties, by the proper sheriffs and other officers of the same counties.