Smokn - Welcome to the forum.
You have an H&R 3rd Model 3rd Variation, circa 1913-'15, this ID from the markings. It appears to be a very nice example - standard 3.25" barrel and Nickel plated finish w/ blued trigger guard. Examining all the excellent pics - it looks as though it wasn't fired much. It was made capable of handling smokeless cartridges - .32 S&W and .32 S&W LONG - NOTE: the freewheeling cylinder (when not cocked) is typical of the AutoEjecting/Automatic models, carried over from circa 1884-1930's - not automatic cylinder stop on that one.
Just for the heck of it - here's a pic of a rare sub-variation of that Auto Ejecting Model, made around the same time as yours.