Dear Heather:
Your rings are marks of corrosions permanently etched in the surface of the stone. They are like shallow chemical scratch, and you can easily agree that you can't remove a scratch with something in a bottle!...
In other words, your rings are surface damages, created by the pH activity of the liquids contained in the glasses that made those rings. And being damages, they have to be repaired, not “removed”.
How?
If they're not too severe, it is possible to do the job with a good-quality Marble Repair Kit; but if they are too severe, you will have to hire a professional stone restoration contractor that will have to first slightly grind (hone) the damaged areas and the polish to blend. It is always worth trying the Marble Repair Kit, though. It will never go bad and it can always become handy.
May I ask you now to please read and e-sign our Statement of Purpose at:
http://www.marblecleaning.org/purpose.htm?
Ciao and good luck,
Mauri
Article ID: 1151
Created On: Tue, Feb 5, 2008 at 5:04 PM
Last Updated On: Tue, Feb 5, 2008 at 12:00 AM
Authored by: Maurizio Bertoli [mail@mbstone.com]
Online URL: https://marblecleaning.org/knowledgebase/article.php?id=1151