Which is useful for, in this case, a fragile silver pendant I had thought to have been lost for good, and had missed very greatly.
How it works:
The aluminum produces ionized particles when heated up with the baking soda.
The aluminum ionized particles bond with the crap that's bound to the silver, much more readily than it binds to the silver.
What you use: just a sheet of aluminum foil in the bottom of a pot; sprinkle on the baking soda. heat water, insert silver, remove silver.
You can just use Very Hot Water from the tap; it takes longer (just soak it for a half-hour). The boiling method is nigh-instantaneous.
Result: a pot full of undrinkable water, and SHININGLY clean silver.
This data brought to me by sinick, who also supplied a kid's science experiement which explains things. PDF file, in case you are a person who objects to such.