Baird,
This Carrara marble can be dry finished with silicone carbide sanding disks applied to an appropriate backer pad on a variable speed grinder. It is a very fast and efficient method. The edges appear to be already shaped and you want to maintain that profile so I would NOT go below 200 grit. At about 2,300 RPM you can start with the 220 to get out deep scratches but don't dwell on any area too long as you will mis-shape the edge. Go to 400 or 500 grit and then to 800, 1500 ( or anything close to those grit stages) and finish with a white cotton buff wheel and a rouge bar. Spin the pad directly onto the rouge bar to pick up rouge in the folds of the cotton wheel and turn RPM's up to about 2,700. You will end up with a very bright edge that maintains it's original shape. Hermes stick on sanding disks work well and can be obtained from most stone tool suppliers. Make sure to use the backer pad with a high degree of flex. You an do this dry because it is outside and the biggest advantage to that is the fact that you can see what you are doing and identify the change in the stone edge as you are working it. Let me know if I can be of further help.
Monte Osterman, Techincal Director-Fabrication
Stone and Tile Pros