The basic function(s) of the quad rail were to free float the barrel for those with accuracy pretensions and to allow the easy installation of all manner of "stuff" many think is essential. My favorite pic of one of those also had a RR hood ornament and a '55 Chevy spotlight attached.

I was gonna do a long sermon on quad rails. Instead, I'll keep it simple: the best rail of that type I've ever encountered was the factory rail on the Ruger piston gun. Round profile of reasonable diameter (with the supplied covers on), came with rubber covers, extras available so you could trim to fit. Wonderful item but you couldn't bolt the kitchen sink to it.