One of the North South line's is the former Cloverleaf division of the Nickel Plate Road, later Norfolk Southern and abandoned about 20 years ago. The other North South line was the Chicago Attica and Southern(former C&EI), but it runs near or close to the NKP line through town and was abandoned about 1948.
This Bridge is along the former Peoria and Eastern Railroad, later part of the Big Four aka New York Central properties, and later Penn Central. It made it into Conrail until about 1982 when abandoned here, and line today doesn't run West of Crawfordsville despite many of the bridges remaining intact. Interesting enough some of the original bricks for the Indianapolis Motor Speedway came from Veedersburg in 1909 via the P&E Railroad's customer "Wabash Clay Company" and would have crossed this bridge en route to the famous "Brickyard" track.
1967 topo shows RR as Penn Central and N-S as Norfolk and Western.
1958 topo shows RR as New York Central.
New York, Chicago, and St. Louis runs through town N-S.
I'm thinking that this bridge was on the former Cleveland, Cincinnati, Chicago and St. Louis Railway (Big Four). The Chicago, Attica, and Southern was further west, and ran north-south.