Cleaning Antique Sterling Silver?

I have a collection of sterling silver napkin rings, which are almost all 100 plus years old. Most have intricate designs in the Art Nouveau style. I have used the aluminum foil/baking soda and salt in hot water method. However, I now have a cloudy white residue left in the creases and indentations of the Repousse Nouveau designs.

How do I get this off without scratching the silver?

By Barbara A