Camphor, a substance distilled from wood chips of the Camphor Tree can be used as an anti-tarnishing agent. This substance is often used in liniments as well. Many pharmacies carry it, and if a small piece of it is placed in the airtight container where your silver jewelry is stored, it draws moisture from the air and reduces tarnishing. Care should be taken when using camphor though, as it is a mild poison and should not be ingested. Make sure to keep it away from the kids. Here is OSHA data regarding camphor: OSHA Info.
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