Welcome to the forum. Based on your description and the patent dates, that could be what is called a .38 Double Action, Second Model. It has an exposed hammer, right? There was a similar model called the safety hammerless that had an enclosed hammer. But it had different patent dates no the barrel and didn't enter production until 1887.
That's a semi-low serial number, so it probably dates to 1880-1881 or somewhere around there. The Double Action was introduced in 1880.