It is a Third Model 1873 Winchester, and the shape of the frame says it is .38-40, so the .40 measurement is spot on. The serial number should be on the bottom tang, behind the lever, and the marking "Model 1873" or later, "Model 1873/Winchester/Trade Mark" should be on the top tang behind the hammer.
The Third Model is the most common 1873, comprising around 630,000 of the total 1873 production of 720,000. Short barrels are common also, as Winchester would put on almost any length barrel a customer wanted, and of course, gunsmiths would also shorten barrels if a customer wanted (during the Model 1873's production life, there was no National Firearms Act and no minimum barrel length). The absence of the fore-end might have been simply a loss, or an attempt to make the rifle look like a Henry for some unknown reason.
The center fire Model 1873 was discontinued in 1919, although some were assembled from parts and sold for a few more years.
Jim
