Every county lying on any navigable river in this State shall extend its jurisdiction from the shore to the channel of the river that divides the counties except where a dividing line has been fixed in such river by law, and, where any ship or other vessel shall be in said river, process may be served on board the said ship or vessel by the officers of either county that can first serve it; but if she is moored or fastened to the land on either side of said river, then she shall be considered as in the county to whose shore she is fastened.