Chris,
The cables are the seat adjuster. They run through the rear channel then around a pulley on the pass. side. A shop manual will have the proper adjustment sequence. Actually, I see you have a '55. An original '55 seat would have a rod running under the center brace. It does the same thing. The design was changed. You probably have a seat frame out of a '48, '49 somewhere in there. Shouldn't matter as long as you have all of the pieces, it's the same size.