Harrington & Richardson's model 1904 was an inexpensive solid-frame pocket revolver, and was that company’s cheapest handgun in a product line that wasn't the best in the first place. The cylinder is not positively locked when you fire the revolver, and you may have noticed that the cylinder can be turned when the trigger is forward.
Generally speaking, accuracy is more coincidental then intentional. Given the relatively high cost of ammunition and the gun’s questionable quality and design, I suggest that you get something else to shoot, and retire this 100 year-old relic to collectable status.
But if you feel otherwise, ammunition is obtainable, but usually has to be special ordered because most retailers don't bother to stock it. Before you order any, be sure that you know what the price will be.