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I presume the number 112,542 is stamped on the gun's butt. If this isn't the case all bets are off.
You have a
Smith & Wesson .32-20 Hand Ejector, Model of 1905, 4th Chg. It was manufactured between 1915 and 1940, within a serial number range running from 65,701 to 144,684 with some 78,893 total made. You have a relatively late serial number suggesting that the revolver was made during the middle 1920's. The .32-20 cartridge was introduced by Winchester for use in their models 1873 and 1892 lever action rifles and carbines.
Standard barrel lengths were 4, 5, and 6 inches. Measure your barrel from the cylinder face to the muzzle end and I think you'll find the length is 5 inches.
Since this is a gun that's been handed down through the family you may want additional information. For a $30.00 fee you can order an historical letter from S&W. Their in-house historian, Roy G. Jinks, will research the original records until he finds your gun, and then send you whatever detalis they have recorded. This usually includes the background history, the revolver's original caliber, barrel length, finish, and to what distributor or dealer it was shipped to along with the date. Additional details are available at:
www.smith-wesson.com