With that blade length and handle composition, it would be a model "244 - 3-1/2", to be read as "model 244 three and a half" and meant that it was a pattern 44 blade, "unbreakable, pearl composition handle", with a 3-1/2" blade. Since the knives were hand ground after stamping out the blanks, the final length of the blade was somewhat variable.
The straight "model 244" had a 4-1/2" blade.
According to reprints of the original catalogs/flyers, this knife was called a "midget knife", meaning that it was smaller than the standard model number knife. It was NOT ever marketed as a "Midget Knife". It was simply described that way in the literature.
The 44 "midgets" were the A44, 244 and X244. A stood for "amber composition non-breakable handles", the 2 represented "solid pearl......" and X2 meant the pearl composition was backed with a layer of black bakelite (called a "special plastic underlay") between the pearl and the tang.
Western's "unbreakable composition handles" were made of a plastic that was in widespread use during the late 1800s-1950s. The commonly used name now is "celluloid", but was it marketed with a variety of names. "Celluloid" was a trademarked brand and since Western did not use the plastic produced by the "Celluloid Manufacturing Company", they couldn't use the term "celluloid" in their marketing, so they used a more generic term, "composition", usually with a descriptor, such as "pearl", "amber", etc. Over time, all celluloidal plastics get brittle, crack and discolor, some faster and/or more severely than others, depending on how they are used and stored. The off-gassing of real celluloid as it deteriorates promotes rusting in steel.
To "restore" the knife to a similar style as the original, all you would need is a couple of appropriately thick pieces of pearl-like plastic, cut them to the size of the tang, mount using 4 steel pins (or just glue the plastic on w/ superglue after cleaning the rust of the tangs) and then gently sand the plastic with very, very fine grit sand paper to round the edges to match the original handle shape, followed by the use of a polishing compound to remove fine scratches.
) for Western knives (my first fixed blade was an L46-5 given to me in August 1965 by my grandfather), watching "ads cut out of magazines" for sale on fleabay, and constantly referring to a book authored by Harlon Platts, grandson of the founder of Western States Cutlery aka Western Cutlery aka Western knives. I also have a bad habit of going through old magazines (and microfilm/fiche copies) at a university library trying to dig out info.