In order to determine if something is ivory most times all you need to do is look very closely at it.
You will need the following items:
Good lighting source
Magnifying glass or jeweler's loupe
Look at the flat parts with minimal carving. Inspect this flat, uncarved area with your magnifier. You are looking for grain patterns or lines known as Schreger Lines.
If you found no lines or patterns at all, do the hot water test.
(Heat water to just under boiling and dip the jewelry in the hot water. Be careful no to dip any glued or metal parts, just the part you are testing, as this could damage the item.
If it is celluloid (ivory substitue) there will be an unmistakable heavy, camphor or menthol smell.
If it is Bakelite there will be an equally unmistakable chemical formaldehyde smell)
Bone is very easy to identify. Unlike teeth and tusks, bones have tiny canals that run through them to carry nutrients to the body and for nerve paths, etc. Some of this organic material adheres to the wall and turns dark as it decays. This material may be hard to see in well bleached pieces however the canals are still there and can be seen when the piece is moved back and forth in strong light.
To sum up; if there are no tiny holes, if Schrerger lines are present and if there is no chemical smell produced by hot water test, then the item is ivory.
I hope this helps you in determining if your piece is ivory, bone or plastic.
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