The patent date is the giveaway! It's a Winchester model 1885. They were made in what is referred to as "Low Walls" and "High Walls", but with the info you've given, it's hard to say which you have.
The barrel may have been changed, or refinished, as it should have had Winchester's rollstamp on the top. Is it round or octagon barreled?
The bottom of the barrel, just in front of the forearm should also have a single number, i.e.-1,2,3,4,5,etc? That is the barrel weight, but it may also not be there, if it has been rebarreled.
If you have a digital camera, you can email me a picture, and I can help with more info.
marlinguy@juno.com

Bob- What you have is a '50's era "varmintized" Winchester low wall.  The barrel and the wood have been replaced.  The serial #84561 should have been 1901 original production.

Bob, there is a strange extra screw in the left side of the receiver.  The lower one (corresponding to a similar one on the right side) holds the trigger tang in place, but I don't recognize the slightly larger one that is above and slightly forward of it.  Your basic receiver is the trim little smooth side (which some call the "thick side" but it isn't) which makes the slickest little basis for a small caliber such as your .22 Hornet (or .22 rimfire, or about any pistol caliber) of any of the 'walls.  Be aware that the lower tang has a distinctly non-factory bend for that varminter stock and will not fit standard low-wall stocks should you ever decide to restock it in the future.  It looks like your rifle escaped many of the indignities that were heaped on some varminters of the day and you got a nice little package.  Hope you will enjoy it a lot, I know I would!   


Regards,
the Green Frog