Things You Will Need
By Hand
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Clean the silver thoroughly of any dust, dirt or other particulates.
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Wet the burnishing tool in the water/soap mixture and, gripping the tool's handle firmly, rub the metal or stone tip of the tool across the surface to be burnished. The tool should be pressed against the silver firmly, as the intent is to use the harder surface (the burnishing tool) to smooth out the softer surface (the silver). If the surface of the silver takes on a slick feel from the soap, wipe it down with the rag to remove the excess before continuing.
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Rinse the silver piece in water and dry thoroughly with a rag once the silver has taken on an adequate shine.
In a Tumbler
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Clean the pound of polished steel shot and the barrel of your tumbler by running the shot and enough solution to cover it (plus a 1/4 inch more) in the tumbler for one hour. Empty the used water and rinse the shot to remove any residue.
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Place the shot, solution to cover (plus 1/4 inch more) and the silver item into the barrel of the tumbler. Turn the tumbler on and let it run for 1/2 hour. Check your silver at the end of that time, and if it has not attained the shine you desire, change your solution and let it run for another 1/2 hour.
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Drain the barrel contents into a colander over a sink. Rinse with water and allow to drain. Remove your silver and dry it thoroughly. Dry your shot thoroughly and store it separate from your tumbler, or put it in the tumbler barrel covered with enough of the solution to keep it protected from the air, which can cause rust.