At risk of repeating information
Smith and Wesson developed, or at least invented, the .22 caliber rimfire around 1856. And the Stevens Company invented the .22 Long Rifle cartridge in about 1887. And, yes, some Winchester 73s were made in .22 caliber. The OP specified .22 but just for a comment...there were bigger caliber rimfires also. The Henry Rifle was powered by .44 rimfire I believe but then the Winchester Company, or someone, quickly developed a centerfire cartridge. I forget who came out with the .22 Long which is not a good cartridge and rarely, if ever, seen anymore. If you search you will find books on the .22 rimfire firearms as I have a couple of them downstairs in my gun books.