What is the advantage of this approach over polishing the silver with an abrasive?
"Silver tarnish is an outer coating of silver sulfide, $\ce{Ag2S}$, formed when silver reacts with trace quantities of air-borne hydrogen sulfide, a smelly gas produced naturally by the digestion of food in living animals. Silver atoms in silver sulfide have lost electrons to sulfur atoms in creating ionic bonds. You can remove this tarnish with home electrochemistry. Convert silver atoms back to their elemental state by restoring their electrons. Sulfur atoms won't relinquish electrons to silver, but with the proper connection, aluminum atoms will. Add about a liter of water with several heaping tablespoons of baking soda to an aluminum pan that has been scoured clean. If you don't have an aluminum pan, use several large strips of aluminum foil at the bottom of another pan. Bring the water to a boil and remove it from the heat source. Slowly immerse a tarnished piece of silver; you'll see an immediate effect as the silver and aluminum make contact. (Add more baking soda if you don't see this.) Also, as silver is brought back to its elemental state, hydrogen sulfide is released back into the air. You'll smell it! The baking soda serves to remove a thin and transparent coating of aluminum oxide, which normally coats aluminum and thus prevent direct contact. The baking soda also serves as a conductive ionic solution to permit the passage of electrons from the aluminum to the silver."
