so as of south bends website, it says that the model number is at the end of the ways by the tail stock. after cleaning the ways off with IPA i found the model number but every place i look including http://www.vintagemachinery.org/mfgindex/detail.aspx?id=1617&tab=5 . Which is rather odd i don’t know if its before 1920 which is when they started serial number naming scheme but im no rocket doctor.
The serial is 34873NCR9
You might find this link to be helpful.
If I’m reading this right, your serial seems to match their post-1947 naming convention.
According to the site, the first block of numbers is the production number, so yours would be the 34,873rd 9" lathe produced.
The first letter is the swing - an N means it’s a 9-inch swing, the second letter is the gear, apron, and drive, where C correlates with a “Standard Change Gear (SCG), Screw Feed Gear, CS”, and the 3rd letter is the spindle and swing type, where an R represents a “Regular Spindle Hole, Standard Swing”.
The final number is the model number.