What model rifle is this?

My grandpa recently bought a golf bag at a garage sale, came home, where to his surprise he found a savage twenty-two long rifle in it. I can't find a serial number on it but there is an inscription on the barrel that reads " manufactured by savage arms Corp. Utica. N. Y. U.s.a patented nov. 28.1905.sep.7.1915. Sep.4.1917. Nov. 20.1917." It's missing a magazine and I want to get one for it but I need to know the model/where the serial number is located. Any information is appreciated.