Welcome to the forum.
You have (as is stamped into the top strap) an H&R SAFETY HAMMER DOUBLE ACTION. It is a 2nd Model made to shoot smokeless/Nitro powder loaded cartridges and in your case the .32 S&W, probably the .32 S&W Long will also fit and fire, if the cylinder is long enough and it was made after 1905 or so, which it was. A serial number in the 88,000 range would, most likely, have been made in early 1906. Your gun is called the "SAFETY HAMMER" because it has the patented H&R spurless hammer (surprised?).
Your piece is missing the cylinder/axis pin and the pin catch assembly, appears to have wooden replacement grips and the Nickel plate is pretty much flaked around the edges - all of which significantly affect the collectibility.
In it's current state, I'd estimate the value to be $US 90 or less.
Do you have any history of how your gun got to NORWAY? I'd be interested in hearing about it.
Here are pics of a couple of pieces from my collection: