Louis,

For me, the aim is to remove any burrs from the inside of the cylinder, and to leave a lightly cross-hatched finish.

I use green 3M Scotchbrite to finish the insides of my cylinders - cut a slot in a dowel, and insert a 2" x 4" strip of Scotchbrite, wind up, put in cylinder and rotate with electric drill.

After cleaning, I burnish a mix (75/25) of sub-micron graphite/0.5u tungsten disulphide into the cylinder surface using a chamois leather mop.

The bores of internal combustion engines are cross hatched, and the premium barrel makers (Krieger, Obermeyer etc.) finish-lap their barrels to ca. 320 'grit', so mirror-polish does not seem the way to go

Have fun & a good Sunday

Best regards

Russ