The main RuneScape Wiki has an article on: Buttons
The Old School RuneScape Wiki also has an article on Buttons.

Buttons can be found by digging level 1 and 3 sites in the Digsite.

If used on Archaeological expert he will say: "Let's have a look. Ah, I think these are from the nobility. Perhaps a royal servant ? Not valuable but an unusual find for this area"

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