I have used the reverse side of some slate tiles for a window-sill, thinking
I could easily remove the marks left by the commercial slate cutter (very
shallow, less than 0.2mm at worst, circular scratches, can't even feel most
of them with my finger nail). Being slate, a soft stone, I thought I would
have no problem.

Oh boy - I've tried using polishing agents like Brasso (left a horrible
mess), sandpaper, wet and dry, high and low speed sanding attachments, an
aluminium oxide sanding disk and lastly an angle-grinder mounted high speed
flap wheel. All to virtually no avail.

Has the cutting process hardened the surface of the tiles in some way ? Does
anyone have any ideas of what else I can try ? I've heard of something
called carborundum paper but never seen any (and B&Q have never heard of
it) - anyone know anything about this ?

Cheers

Stephen